過去作文曾有所謂『起承轉合』之論，然而天下文章天下人寫，又何必拘泥於『套式』的呢？倘若一招半式尚未學習，又何彷拘泥於『套式』的呢！終究寫作者之表述，需要閱讀者能明白，所以詞能達意、議論清楚、文字通順 …… 其初始，足矣哉。

有答之問之所生，或在原理不能貫通、習焉而未能察、概念內蘊尚無法甚解 …… ，因作此破題之問︰

【既知】

假使一個任意複雜之光學系統竟能夠『等效』於一片『薄透鏡』豈非太美妙耶！且聽聽 Justin Peatross 和 Michael Ware 先生們之大哉論也

※ 註︰ 若一光學系統光線進、出介質折射率相同，則

。

顯然 不等於零。

─── 摘自《光的世界︰矩陣光學六戊》

 

【已知】

前三篇文本中，我們談了一般『光學矩陣』

只要 ，都可借著『自由空間』

化成一個等效之『薄透鏡』

。

因此在『主平面』之參考系裡，分享著同樣的『成像公式』

，具有相同『成像條件』， 參數為

。

甚至可以『串接成像』

的矣！如是就確定了參數 之『聚焦』地位，以及參數 的『影像縮放』性質！！

─── 摘自《光的世界︰矩陣光學六庚》

 

【且知】

現象既因相距 之兩透鏡之組合而起︰

物 → 光 …… → 透鏡 → 距離 → 透鏡 …… → 像

且先列出其『光學矩陣』表達式︰

已知若其『等效』於『薄透鏡』，焦距 等於 。所以曉

‧ 時， 。

‧ 或 時，組合焦距可由該式算出。

因是問題就落在 的時候了。但思此刻之前、之後恰是 變號之際，也是組合透鏡或聚、或散性質變化之處，故而特殊的耶！！？？

─── 摘自《光的世界︰矩陣光學六壬》

 

莫非是原理不足以解釋現象成因的呢？？還是條件太過複雜以至於難以解析耶！！或因為『薄透鏡』之理想性而想入非非的乎︰

若問為什麼平面上的一個一般三角形可以如下圖表示

， 只用著 三個參數？即使在思考過 是『底』之『長』， 是此『底』之『高』， 是此『高』距與此『底』一端的距離。我們深信這就『確定』了那個三角形。然而若再問︰如果此三角形的三個頂點用更一般的   、 、 來表達 ，如是分明有六個參數。那麼這兩種『表述』當真是一樣的嗎？設想你在桌面上『移動』一個三角形，從此『位置』此『方位』到達彼『位置』彼『方位』，你會認 為這個三角形『改變』了嗎？？假使『直覺』以為『不變』，這個三角形就必得有使之『不變』的『因由』，這個『因由』不必『參照』解析幾何的『座標』而確立 。或可說它就是歐式幾何一個三角形的『定義』內涵而已。如此而言，一個『確定』的三角形，可由它的三個『邊長』來『確立』，所以六個參數補之以三個確定之 邊長關係，豈非還是三個參數的耶？？

因為這個『歐式幾何』的『留白』，常使人懷疑『解析幾何』簡化『座標系』的『選擇』，到底『圖形』的『自由度』是幾何的了。說難道易，就請讀者思索︰平面上的『 □ 』與『 ○ 』，到底一方一圓需要幾個參數來描述的呢？

從物理上講，那個三角形就是『剛體』 rigid body ，它在『運動』中保持『形狀』的『不變性』。

─── 摘自《勇闖新世界︰ W!o《卡夫卡村》變形祭︰品味科學‧教具教材‧【專題】 PD‧箱子世界‧留白》

 

現象之理則的推演千絲萬縷，其歸結唯一而已矣☆

 

 

 

 

 

 

 

 

 

 

易‧繫辭上

易曰「自天祐之，吉，无不利」。子曰：「祐者，助也。」天之所助者順也，人之所助者信也。履信思乎順，又以尚賢也。是以自天祐之，吉，无不利也。子曰：「書不盡言，言不盡意。」然則聖人之意，其不可見乎？子曰：「聖人立象以盡意，設卦以盡情偽，繫辭以盡其言，變而通之以盡利，鼓之舞之以盡神，乾坤其易之縕邪 ？」乾坤成列，而易立乎其中矣，乾坤毀，則无以見易。易不可見 ，則乾坤或幾乎息矣。是故，形而上者謂之道，形而下者謂之器，化而裁之謂之變，推而行之謂之通，舉而錯之天下之民，謂之事業 。是故，夫象，聖人有以見天下之賾，而擬諸其形容。象其物宜，是故謂之象。聖人有以見天下之動，而觀其會通，以行其典禮，繫辭焉以斷其吉凶，是故謂之爻。極天下之賾者存乎卦，鼓天下之動者存乎辭，化而裁之存乎變，推而行之存乎通，神而明之存乎其人 。默而成之，不言而信，存乎德行。

莊子‧外物

荃者所以在魚，得魚而忘荃；蹄者所以在兔，得兔而忘蹄；言者所以在意，得意而忘言。吾安得夫忘言之人而與之言哉！

 

東晉時陶淵明在《五柳先生傳》中寫到︰

好讀書，不求甚解；毎有會意，便欣然忘食。

是否深知『書不盡言，言不盡意。』？深了『言者所以在意，得意而忘言。』的呢？？單單『不求甚解 』一詞如何解釋往往南轅北轍的哩！有人認為是淺嘗輒止式的不清不楚。也有人以為是虛懷若谷般的自謙之言。直叫人對此『不求甚解 』之詞，來個不求甚解 的了 ！！若問︰既然想『淺嘗輒止』，幹嘛要『好讀書』？假使想自謙『虛懷若谷』，也許會講自己沒讀過幾本書的吧！更何況一句話的意義，需要前言後語通讀，不可隨意斷章取義，否則『每有會意』之『每』意指『每每』？或許與『淺嘗輒止』者矛盾矣？？其實此『每每』者正如《論語》《學而》篇之『學而時習之』者，早曉得輪扁斲輪之故事︰

桓公讀書於堂上，輪扁斲輪於堂下，釋椎鑿而上，問桓公曰：『敢問：公之所讀者，何言邪？』公曰：『聖人之言也。』曰：『聖人在乎？』公曰：『已死矣。』曰：『然則君之所讀者，古人之糟魄已夫！』桓公曰：『寡人讀書，輪人安得議乎！有說則可，無說則死！』輪扁曰：『臣也以臣之事觀之。斲輪，徐則甘而不固，疾則苦而不入，不徐不疾，得之於手而應於心，口不能言，有數存焉於其間。臣不能以喻臣之子，臣之子亦不能受之於臣，是以行年七十而老斲輪。古之人與其不可傳也死矣，然則君之所讀者，古人之糟魄已夫！』

以至於︰

古之學者為己。然而問『學』之『道』貴在能『心有疑』又還『感覺怪』，『去疑除怪』以至於『哈哈大笑』幽默一番，有益於『身心健康』。故

─── 所謂文字，得意忘言，能不能傳，誰知誰了？！ ───

就像金文裡有『』甚字，《說文解字》講：甚，尤安樂也。从甘，从匹耦也。，古文甚。焉知為何字義竟從『安樂』變成『過度』的耶？？！！所以『每每者』今日不解，明日再解；日日解之不解，待時趁機而解。這才謂『不求甚解者』乎！！？？

因此學習者能由自己的學習過程中知道︰從一般原理

前三篇文本中，我們談了一般『光學矩陣』

只要 ，都可借著『自由空間』

化成一個等效之『薄透鏡』

。

因此在『主平面』之參考系裡，分享著同樣的『成像公式』

，具有相同『成像條件』， 參數為

。

甚至可以『串接成像』

的矣！如是就確定了參數 之『聚焦』地位，以及參數 的『影像縮放』性質！！

─── 摘自《光的世界︰矩陣光學六庚》

 

到推導說明具體物件之設計概念與應用想法，尚須下功夫也。

既有上篇範例，也有《光的世界︰【□○閱讀】話眼睛《一》》之系列文本，且題一問，邀請讀者嘗試解讀維基百科放大鏡詞條︰

Magnifying glass

A magnifying glass (called a hand lens in laboratory contexts) is a convex lens that is used to produce a magnified image of an object. The lens is usually mounted in a frame with a handle (see image).

A sheet magnifier consists of many very narrow concentric ring-shaped lenses, such that the combination acts as a single lens but is much thinner. This arrangement is known as a Fresnel lens.

A magnifying glass can also be used to focus light, such as to concentrate the sun’s radiation to create a hot spot at the focus for fire starting.

The magnifying glass is an icon of detective fiction, particularly that of Sherlock Holmes.

Text seen through a magnifying glass

History

The earliest evidence of a magnifying device was a joke in Aristophanes‘s The Clouds from 424 BC, where magnifying lenses to start kindling were sold in a pharmacy, and Pliny the Elder‘s “lens”, a glass globe filled with water, used to cauterize wounds. (Seneca wrote that it could be used to read letters “no matter how small or dim”).^[1] Roger Bacon described the properties of a magnifying glass in 13th-century England. Eyeglasses were developed in 13th-century Italy.^[2]

Magnification

The magnification of a magnifying glass depends upon where it is placed between the user’s eye and the object being viewed, and the total distance between them. The magnifying power is equivalent to angular magnification (this should not be confused with optical power, which is a different quantity). The magnifying power is the ratio of the sizes of the images formed on the user’s retina with and without the lens.^[3] For the “without” case, it is typically assumed that the user would bring the object as close to one eye as possible without it becoming blurry. This point, known as the near point, varies with age. In a young child, it can be as close as 5 cm, while, in an elderly person it may be as far as one or two metres. Magnifiers are typically characterized using a “standard” value of 0.25 m.

The highest magnifying power is obtained by putting the lens very close to one eye and moving the eye and the lens together to obtain the best focus. The object will then typically also be close to the lens. The magnifying power obtained in this condition is MP₀ = (0.25 m)Φ + 1, where Φ is the optical power in dioptres, and the factor of 0.25 m represents the assumed near point (¼ m from the eye). This value of the magnifying power is the one normally used to characterize magnifiers. It is typically denoted “m×”, where m = MP₀. This is sometimes called the total power of the magnifier (again, not to be confused with optical power).

However, magnifiers are not always used as described above because it is more comfortable to put the magnifier close to the object (one focal length away). The eye can then be a larger distance away, and a good image can be obtained very easily; the focus is not very sensitive to the eye’s exact position. The magnifying power in this case is roughly MP = (0.25 m)Φ.

A typical magnifying glass might have a focal length of 25 cm, corresponding to an optical power of 4 dioptres. Such a magnifier would be sold as a “2×” magnifier. In actual use, an observer with “typical” eyes would obtain a magnifying power between 1 and 2, depending on where lens is held.

Diagram of a single lens magnifying glass.

Magnifying glass on an arm lamp

 

的內容☆

 

 

 

 

 

 

 

 

 

 

 

知道一個公式

New closest point =

，明白它的意義，而且能夠應用，也許通常已經足夠。然而說理解來源與出處，是講這公式之由來，曉得該如何從 □○ 原理將之推導出來。如是可將理論與應用結合起來，往往也是創新的基礎材料。此處藉著註解維基百科『近攝鏡』 Close-up filter 之詞條，講講這個實務︰

Close-up filter

In photography, a close-up filter, close-up lens or macro filter is a simple secondary lens used to enable macro photography without requiring a specialised primary lens. They work identically to reading glasses, allowing any primary lens to focus more closely. It is actually more appropriate to use the close-up lens terminology as it is a lens and not a filter, although close-up lenses typically mount on the filter thread of the primary lens, and are manufactured and sold by suppliers of photographic filters. Some manufacturers refer to their close-up lenses as diopters, after the unit of measurement of their optical power.

為什麼要叫 filter 不叫 lens 呢？因為它裝在用膠卷之『傳統相機』 的『濾光器』位置︰

濾光器是一種對光的不同波段具有選擇性吸收的光學元件。常見的有有色玻璃、染色膠片或者充滿有顏色溶液的玻璃槽等幾種形式。其中用有色玻璃或染色膠片製成的濾光器也稱為濾光片/鏡、濾色片/鏡等。廣泛用於攝影、電氣照明等領域。

 

過去一般也是作『濾光器』公司所製造。選擇安裝時必須符合各家不同之『鏡頭接口』規範︰

Lens mount

A lens mount is an interface — mechanical and often also electrical — between a photographic camera body and a lens. It is confined to cameras where the body allows interchangeable lenses, most usually the rangefinder camera, single lens reflex type or any movie camera of 16 mm or higher gauge. Lens mounts are also used to connect optical components in instrumentation that may not involve a camera, such as the modular components used in optical laboratory prototyping which join via C-mount or T-mount elements.

 

雖然樹莓派的 RaspiCAM 可說是種 WebCAM ，不過它的設計並未考慮讓人擴張或者更換鏡頭︰

S-mount (CCTV lens)

The S-mount is a standard lens mount used in various surveillance CCTV cameras and webcams. It uses a male metric M12 thread with 0.5 mm pitch on the lens and a corresponding female thread on the lens mount; thus an S-mount lens is sometimes called an “M12 lens”. Because the lens mounts are usually attached directly to the PCB of the sensor, the standard is often called “board lens”. The supported sensor formats range from the smallest 1/6-inch type to the largest 2/3-inch having an 11mm diagonal sensor. The lens mount is usually made of plastic and the lenses lack an iris control. S-mount lenses do not have a flange and therefore there is no fixed lens to sensor distance and they must be adjusted to focus.^[1]

S-mount camera PCB. The right one with lens detached shows a 1/3″ CCD sensor. Spring is used to push and secure the lens when mounted.

 

就如智慧型手機一樣，大概只能用『夾住式』 clip-on 機制的鏡頭 lens 了︰

 

While some single-element close-up lenses produce images with severe aberrations, there are also high-quality close-up lenses composed as achromatic doublets which are capable of producing excellent images, with fairly low loss of sharpness.

到底要如何減少各種『像差』呢？比方說消除『色差』之法！

雙合透鏡

雙合透鏡是將兩片單透鏡結合在一起的光學設計。這兩片透鏡分別用折射率和色散都不同的玻璃製成，通常一片是冕牌玻璃（Crown glass），另外一片是燧石玻璃（flint glass）。這樣的組合產生的影像品質比單一透鏡好。而早已滅絕的三葉蟲，擁有由方解石構成的天然的雙合透鏡。

雙合透鏡有許多不同的形式，但多數商用的雙合透鏡都是消色差透鏡，主要用於減少色差，同樣也減少球面像差和其他在光學系統上的像差；複消色差透鏡也可以用雙合透鏡製造。

膠合的雙合透鏡，透鏡是以膠黏劑相結合，例如加拿大冷杉香脂或環氧。有些在透鏡之間不使用膠黏劑，而依靠外部的固定物使它們結合在一起，這種稱為氣隙雙合透鏡（air-spaced doublets）。

一個消色差的雙合透鏡。

 

Close-up lenses are usually specified by their optical power, the reciprocal of the focal length in meters. Several close-up lenses may be used in combination; the optical power of the combination is the sum of the optical powers of the component lenses; a set of lenses of +1, +2, and +4 diopters can be combined to provide a range from +1 to +7 in steps of 1. A split diopter has just a semicircular half of a close-up lens in a normal filter holder. It can be used to photograph a close object and a much more distant background, with everything in sharp focus; with any non-split lens the depth of field would be far too shallow.

若是知道何謂『屈光度』的耶？了解了『完美成像』之條件！以及明白可接受清晰度之『模糊圈』的論證？？！！那麼

一個詞條︰

Deep focus

Deep focus is a photographic and cinematographic technique using a large depth of field. Depth of field is the front-to-back range of focus in an image — that is, how much of it appears sharp and clear. Consequently, in deep focus the foreground, middle-ground and background are all in focus. This can be achieved through use of the hyperfocal distance of the camera lens.

Deep focus is achieved with large amounts of light and small aperture. It is also possible to achieve the illusion of deep focus with optical tricks (split focus diopter) or by compositing two pictures together. It is the aperture of a camera lens that determines the depth of field. Wide angle lenses also make a larger portion of the image appear sharp. The aperture of a camera determines how much light enters through the lens, so achieving deep focus requires a bright scene or long exposure. Aperture is measured in f-stops (T-stops on lenses for motion picture cameras are f-stops adjusted for the lenses’ light transmission, and cannot be used directly for depth of focus determination) with a higher value indicating a smaller aperture.

The opposite of deep focus is shallow focus, in which only one plane of the image is in focus.

Orson Welles and Gregg Toland were most responsible for popularizing deep focus through its use in Welles’s film Citizen Kane.^[1]

This image has deep focus, as everything from foreground to sky is visible in full detail.

 

一篇文章︰

《Deep Focus vs. Split Diopter》

是否足以解讀該文本之敘述乎！！？？

 

Optical scheme of close-up photography.
1 – Close-up lens.
2 – Camera objective lens (set to infinity).
3 Camera.
4 – Film or CCD plane.
y – Object
y” – Image

 

一個固定焦距 的相機，由於感光膠卷、CCD  或 CMOS 之成像位置 也是固定的。假設以等效主平面之薄透鏡成像條件︰

來作考察，唯有一個物距 能夠完美成像。若是相機的鏡頭不能夠前進後退調整聚焦，那麼通常會設定聚焦於超焦距  hyperfocal distance 之物距︰

，以得 到 的物件，成像都能有可接受之清晰度。

所以我們可以知道下面文字

focusing to infinity

意指 ， 此時成像面 就是 焦距面︰

。

When you add a close-up lens to a camera which is focusing to infinity, and you don’t change the focus adjustment, the focus will move to a distance which is equal to the focal length of the close-up lens. This is the maximal working distance at which you will be able to take a picture with the close-up lens. It suffices to divide 1 by D, the diopter value of the close-up lens, to get this maximal working distance in meters:

Sometimes that distance is also given on the filter in mm. A +3 filter will have a maximal working distance of 0.333 m or 333 mm.

 

如是假設近攝鏡 與相機鏡頭緊貼，組合系統可以用等效薄透鏡 來描述︰

。

當其它條件維持不變，此時能夠完美成像織物距 將滿足︰

。

The magnification reached in those conditions is the focal distance of the objective lens (f) divided by the focal distance of the close-up lens, i.e. the focal distance of the objective lens, in m, multiplied by the diopter value (D) of the close-up lens:

In the example above, if the lens has a 300 mm focal distance, magnification is equal to 0.3*3 = 0.9.

Given the small size of most sensors (about 25 mm for APS C sensors) a 20 mm insect will almost fill the frame at this magnification. Using a zoom lens makes it easy to frame the subject as desired.

在此條件下，此系統的放大率

。

為什麼要稱之為 的呢？這可由底下類似的推導，當 之極限值得知其意義。

When you add a close-up lens to a camera which is focusing at the shortest distance at which the objective lens can focus, and you don’t change the focus adjustment, the focus will move to a distance which is given by following formula:

X being the shortest distance at which the objective lens can focus, in m, and D being the Diopter value of the close up filter. This is the minimal working distance at which you will be able to take a picture with the close-up lens.

For example, a lens that can focus at 1.5 m combined with a +3 diopter close up lens will give a closest working distance of 1.5/(3*1.5+1)=0.273 m.

已知

而且 。從 ，解之得

。所以

。

 

如果讀者明白

，

了解

。

自可證明下式且求得極限的吧！！？？

The magnification reached in those conditions is given by following formula:

M_X being the magnification at distance X without the close-up lens.

In the example above, the gain of magnification at X_min will be (3*1.5 + 1)= 5.5.

It is at this X_min distance that you will get the highest magnification.

To use a close up filter it is important to know those maximal and minimal distances, because only if you are within that range it will be possible to take a shot. There is not much of a range between the minimum and maximum values and the difference in magnification is quite moderate also.

The close up filters can turn telephoto lenses in macro lenses with a large working distance to prevent scaring small animals and a second advantage is the small size of the background making it easier to isolate the subject from messy surroundings. To use the filters for animals the size of the animal will determine the working distance (small snakes 1 m to 50 cm, lizards 50–25 cm, small butterflies, beetles 25–10 cm), so it is essential to know what will be the favorite subject before screwing on a close up filter. The close up filters are most effective with long focal length objectives and using a zoom lens is very practical to have some flexibility in the magnification. A good technique for sharp focussing is to take a picture at a long focal length first to have optimal sharpness at the essential details and then zooming out to have the desired size in the frame.

 

 

 

 

 

 

 

 

 

 

 

三年前樹莓派論壇上有篇名為

《Camera focus distance and macro lenses》

……

……

───

 

的主題文章，就此展開 RaspiCam

【允許相機】︰
Enable Camera

樹莓派上有一個『 CSI 』 連接器，用來連接相機模組。它需要 GPU 上的『韌體』firmware 支援，這個選項可以『啟用』或『禁用』這個支援。目前樹莓派上提供了三個命令列的應用程式 raspistill ， raspivid 和 raspistillyu 。你可以到這裡下載『RaspiCam Documentation』使用手冊。

─── 摘自《raspi-config 再探！！》

近攝鏡

近攝鏡（Close-up filter）是一個簡單的二次使用鏡頭（secondary lens），可以安裝在普通鏡頭前實現微距拍攝，而無需使用專門的微距鏡頭。近攝鏡安裝後，可將鏡頭的放大比例增大，讓相機的最近對焦距離得以縮短，得到放大比例的成像。

簡單的近攝鏡可能僅有單片凸透鏡，會造成像差；較為複雜的近攝鏡可能帶有雙合透鏡結構以獲得出色的成像。

三組近攝鏡

傳統的近攝鏡

之討論與應用。

雖然現今尚且無法明白《卡夫卡村》的三光眼鏡到底如何製造︰

不知何時 Mrphs 遞給了我一副眼鏡，說道︰這是小學堂『教具室』研發的『三光眼鏡』，可以觀看而且調變『可見光』、『紅外線』 、『紫外線』的影像顯示。直須戴上就好，和貴處普通眼鏡一般。戴上後，向著『幽竟夢卿』望去，當真是目瞪口呆。只見

星空綺麗

This infrared space telescope image has (false color) blue, green and red corresponding to 3.4, 4.6, and 12 µm wavelengths, respectively.

砂石熒熒

A collection of mineral samples brilliantly fluorescing at various wavelengths as seen while being irradiated by UV light.

草木含情。

心思這個世界在不同的光照下竟會是那麼的奇特美麗。心想為何要叫做『三光』的呢？『教具室』是何處的耶？？剛打算開口問，就聽 Mrphs 講︰『三光』之名來自《三字經》的

三才者，天地人。三光者，日月星。

意在研究『日月星』的『光譜』與『生命』之關係。當地人都知道這個『教具室』雖只致力研發『教具』與『教材』，事實上卻是《卡夫卡村》尖端之科技的代表，推動『科學教育』目標之實踐。努力『科技護生』宗旨之完成。因此才催促先生快點前行的哩。

今夕何夕欲語無言，只能說光一個『 Infragram 』就需鼓吹多年，

─── 摘自《勇闖新世界︰ W!o《卡夫卡村》變形祭︰感知自然‧幽夢‧四》

 

眼下令人好奇的是

New closest point = x/(Dx +1)

到底打從哪來？？

 

 

 

 

 

 

 

 

 

 

 

戰國策‧趙一

《張孟談既固趙宗》

張孟談既固趙宗，廣封疆，發五百，乃稱簡之途以告襄子曰：「昔者，前國地君之御有之曰：『五百之所以致天下者約，兩主勢能制臣，無令臣能制主。故貴為列侯者，不令在相位，自將軍以上，不為近大夫。』今臣之名顯而身尊，權重而眾服，臣愿捐功名去權勢以離眾。」襄子恨然曰：「何哉？吾聞輔主者名顯，功大者身尊，任國者權重，信忠在己而眾服焉。此先聖之所以集國家，安社稷乎 ！子何為然？」張孟談對曰：「君之所言，成功之美也。臣之所謂 ，持國之道也。臣觀成事，聞往古，天下之美同，臣主之權均之能美，未之有也。前事不忘，後事之師。君若弗圖，則臣力不足。」愴然有決色。襄子去之。臥三日，使人謂之曰：「晉陽之政，臣下不使者何如？」對曰：「死僇。」張孟談曰：「左司馬見使於國家 ，安社稷，不避其死，以成其忠，君其行之。」君曰：「子從事。 」乃許之。張孟談便厚以便名，納地、釋事以去權尊，而耕於負親之丘。故曰，賢人之行，明主之政也。

耕三年，韓、魏、齊、燕負親以謀趙，襄子往見張孟談而告之曰：「昔者知氏之地，趙氏分則多十城，復來，而今諸侯孰謀我，為之奈何？」張孟談曰：「君其負劍而御臣以之國，舍臣於廟，授吏大夫，臣試計之。」君曰：「諾。」張孟談乃行，其妻之楚，長子之韓，次子之魏，少子之齊。四國疑而謀敗。

 

集集大地震震醒夢中人，至今時隔十七年，有人揮不去哀愁！雖說天災難料，人禍豈是不可免耶？所以古人講︰前事不忘，後事之師 。如果耳聰目明是謂聰明，焉能聰明反被聰明誤乎？？！！

現在的人『用眼』『用耳』過度；飲食的『口味』又太重，或許該想想這樣做，難道就真的是沒『後果』的嗎？也許老子《道德經》中的一段話，頗值得今人來思考︰
第十二章

五色令人目盲；五音令人耳聾；五味令人口爽；馳騁畋 ㄊㄧㄢˊ獵，令人心發狂；難得之貨，令人行妨。是以聖人為腹不為目，故去彼取此。

這個『突然變化』的理論，正是理解『橋樑』為何會『斷裂』，又怎是在『此時』的科學說明。常常人們有一種『天真』的想法，以為人事物『昨天』如此，『今天』也如此；『明天』『必然』如此。但事實上，明天只能是『或然』如此的吧！！同時這個理論也補足講解了『老化』曲線的『死亡點』將『在那裡』等著結束這條曲線，終將不可能一直持續磨耗，定然會有一個壽限！！

之前講『古人說︰信之大可及於豚魚』出之於《易經》，不知今日讀來是否會有『戚戚焉』？？

中孚：豚魚吉，利涉大川，利貞。

彖曰：中孚，柔在內而剛得中。 說而巽，孚，乃化邦也。 豚魚吉 ，信及豚魚也。 利涉大川，乘木舟虛也。 中孚以利貞，乃應乎天也。

象曰：澤上有風，中孚﹔君子以議獄緩死。

初九：虞吉，有他不燕。
象曰：初九虞吉，志未變也。

九二：鳴鶴在陰，其子和之，我有好爵，吾與爾靡之。
象曰：其子和之，中心愿也。

六三：得敵，或鼓或罷，或泣或歌。
象曰：可鼓或罷，位不當也。

六四：月几望，馬匹亡，無咎。
象曰：馬匹亡，絕類上也。

九五：有孚攣如，無咎。
象曰：有孚攣如，位正當也。

上九：翰音登于天，貞凶。
象曰：翰音登于天，何可長也。

─── 摘自《目盲與耳聾》

 

這裡且先列出常見之眼疾︰

近視

近視（英語：Myopia）是指眼睛看近處清楚而看遠處不清楚的一種病理狀態。有近視的人在看遠處時，平行於視軸的平行光線通過眼球屈光系統的折射，彙聚在視網膜前，不能在視網膜上形成清晰的成像，因此無法看清，屬於一種屈光不正；而在看近處的物體時，像會後移到視網膜上，從而可以看清。近視的人，通過眯起眼睛可以限制光線的入射，從而減小像差，使自己可以看得更清楚一些 ，myopia原來的意思是眯著眼睛。近視後的遠視力可以透過凹透鏡來矯正，通常用屈光度來衡量屈光不正的程度，0到-3.00D屬於輕度近視，-3.00到-6.00D屬於中度近視，高於-6.00D的則是高度近視。高度近視眼的人因為眼軸過長而屬於一些眼病的高危人群，例如視網膜脫落和青光眼。

凹透鏡對近視的遠視力的矯正。

 

近視者看到的圖像（左），正常視力者看到的圖像（右）。

遠視

遠視（Hypermetropia, Hyperopia）是指平行光線經過眼的屈光介質在視網膜後聚焦的不正常屈光狀態。輕度遠視的患者因為眼的調節功能大多不會有癥狀，40歲左右的輕度患者因為調節功能下降會看不清近距離的事物；中度和重度的患者因為接近或超過眼的調節能力無論遠近都不清晰。

近視是相似但方向相反的情況。

使用遠視眼鏡（凸透鏡）矯正遠視眼。

散光

散光（又稱亂視，小兒散光，散光眼，Astigmatism）散光是眼睛的一種屈光不正常表現，與角膜的弧度有 關。有些人眼睛的角膜在某一角度區域的弧度較彎，而另一些角度區域則較扁平。造成散光的原因，就是由於角膜上的這些厚薄不勻或角膜的彎曲度不勻而使得角膜 各子午線的屈折率不一致，使得經過這些子午線的光線不能聚集於同一焦點，光線不能準確地聚焦在視網膜上形成清晰的物像 ，這種情況稱為散光。

人類的眼睛並不是完美的，如果角膜在某一角度的弧度較彎，而另一些角度則較扁平，光線便不能準確地聚焦在視網膜上，這種情況便稱為散光。散光患者看東西時會較難細微地看清景物。一般情況下，散光並不會獨自出現，患者的眼睛通常都會伴有近視或遠視。

規則散光多數是由於角膜先天性異態變化所致，還可能存在晶狀體散光。也有些後天引起的散光，比如眼瞼長針眼或粟粒腫，長期用眼姿勢不良（如經常眯眼、揉眼、躺著看書等等），這樣眼皮壓迫角膜也會使角膜弧度改變，發生散光並使散光度數增加，另外，一些眼科手術如白內障及角膜手術也可能改變散光的度數及軸度。 不規則散光主要由於角膜屈光面凹凸不平所致，如角膜潰瘍、瘢痕、圓錐角膜、翼狀胬肉等。

散光患者在不同距離所見文字

老花

老花（Presbyopia）是眼睛出現老化而導致晶狀體不能對近物對焦的視力問題。患者因而在看近物時視物變得模糊。

Presbyopia

 

然後以

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。

……

pi@raspberrypi:~  f_{eye} = f_2 f_{fix} = f_1 f_{eff}  \frac{1}{f_{eff}} = \frac{1}{f_{fix}} + \frac{1}{f_{eye}} - \frac{L}{f_{fix} \cdot f_{eye}} D_{eff} =  D_{f_{fix}} + D_{f_{eye}} - L \cdot D_{f_{fix}} \cdot D_{f_{eye}}d_{obj}d_{img} \frac{1}{d_{obj}} + \frac{1}{d_{img}} = \frac{1}{f_{eye}} \approx 10 - 20 \ mm \frac{1}{d_{obj}} + \frac{1}{d_{new-img}} = \frac{1}{f_{eff}} d_{new-img}$ 輕輕鬆鬆落在視網膜上的吧☆