每日彙整: 2016-09-08

樹莓派、樹莓派之學習、樹莓派之教育

光的世界︰【□○閱讀】話眼睛《八》

莊子‧《外物》

惠子謂莊子曰：「子言無用。」莊子曰：「知無用而始可與言用矣 。夫地非不廣且大也，人之所用容足耳。然則廁足而墊之，致黃泉 ，人尚有用乎？」惠子曰：「無用。」莊子曰：「然則無用之為用也亦明矣。」

莊子曰：「人有能遊，且得不遊乎？人而不能遊，且得遊乎？夫流遁之志，決絕之行，噫！其非至知厚德之任與！覆墜而不反，火馳而不顧，雖相與為君臣，時也，易世而無以相賤。故曰：至人不留行焉。夫尊古而卑今，學者之流也。且以豨韋氏之流觀今之世，夫孰能不波？唯至人乃能遊於世而不僻，順人而不失己，彼教不學，承意不彼。

目徹為明，耳徹為聰，鼻徹為顫，口徹為甘，心徹為知，知徹為德 。凡道不欲壅，壅則哽，哽而不止則跈，跈則眾害生。物之有知者恃息，其不殷，非天之罪。天之穿之，日夜無降，人則顧塞其竇。胞有重閬，心有天遊。室無空虛，則婦姑勃谿；心無天遊，則六鑿相攘。大林丘山之善於人也，亦神者不勝。

德溢乎名，名溢乎暴，謀稽乎誸，知出乎爭，柴生乎守，官事果乎眾宜。春雨日時，草木怒生，銚鎒於是乎始修，草木之到植者過半 ，而不知其然。

靜然可以補病，眥搣可以休老，寧可以止遽。雖然，若是，勞者之務也，非佚者之所未嘗過而問焉。聖人之所以駴天下，神人未嘗過而問焉；賢人所以駴世，聖人未嘗過而問焉；君子所以駴國，賢人未嘗過而問焉；小人所以合時，君子未嘗過而問焉。

演門有親死者，以善毀，爵為官師，其黨人毀而死者半。堯與許由天下，許由逃之；湯與務光天下，務光怒之。紀他聞之，帥弟子而踆於窾水，諸侯弔之三年，申徒狄因以踣河。

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。吾安得忘言之人而與之言哉？」

 

固然立足之地足以容人，若將足側之地下掘至黃泉，如是容人餘地尚有用乎？莊子非但深曉當其無何謂也！！

傳聞有一回愛因斯坦突發奇想，想將『雜訊』放大，人們都覺得很奇怪，幹嘛要把『沒用的』雜訊放大？難道愛因斯坦很了解『當其無』嗎︰

『老子道德經 第十一章』

三十輻，共一轂，當其無，有車之用。

埏埴以爲器，當其無，有器之用。

鑿戶牖以爲室，當其無，有室之用。

故有之以爲利，無之以爲用。

或許應該說如果沒有『無所不在』的雜訊，又怎麽能製作『任意頻率』── 放大雜訊，用慮波器選擇所要的頻率 ── 的振盪器呢？恰可比美於所謂的『腦力激盪』之法。

─── 摘自《制器尚象，恆其道。》

 

甚知心靈濾波器的耶？？

夫尊古而卑今，學者之流也。且以豨韋氏之流觀今之世，夫孰能不波？唯至人乃能遊於世而不僻，順人而不失己，彼教不學，承意不彼。

為何暗箱能夠呈像？感光相紙無法靠著近物取像？？需要選擇想要過濾不想要光束之孔徑也！幾何光學所談近軸近似，暗寫有物管此近與不近耶？然而豈可得其矩陣表達式的呢！因是知虹膜不祇美，瞳孔也絕非僅是一洞，實是為生物之利與用矣！！

且讓我們循著歷史之足跡︰

模糊圈

模糊圈，攝影術用語，又叫彌散圓(circle of confusion)。

點光源經過鏡頭在焦平面成的像是一個點，保持鏡頭與底片距離不變，沿光軸方向前後移動點光源，像平面上成的像就會成為有一定直徑的圓形，圓形的大小取決於鏡頭孔徑和點光源偏離程度，只要這個圓形像的直徑足夠小，相片看去仍然夠清晰，點光源圓形像再大些，相片會顯得模糊，這個臨界點光源圓形像，就叫模糊圈。

在焦點附近，光線還未聚集到一點，點的影象成為模糊的一個圓，這個圓就叫做彌散圓。 在現實當中，觀賞拍攝的影象是以某種方式(比如投影、放大成照片等等)來觀察的，人的肉眼所感受到的影象與放大倍率、投影距離及觀看距離有很大的關係，如 果彌散圓的直徑小於人眼的鑑別能力，在一定範圍內實際影象產生的模糊是不能辨認的。這個不能辨認的彌散圓就稱為容許彌散圓(permissible circle of confusion)。

一般35毫照相機鏡頭的模糊圈直徑=1/30毫米，中幅相機鏡頭的模糊圈直徑=1/15毫米，微型相機的模糊圈直徑=1/60毫米。但是各照相機廠所定的模糊圈直徑，會略微不同，宜參考照相機說明書。

模糊圈的概念首先由1866年英國攝影雜誌署名T.H發表的一篇文章提出來的，他通過實驗發現人眼在25厘米明視距離看圖，可以分辨圖中相距為 1/4毫米的兩條線。一張35毫米照相機底片放大成20×30厘米相片(即放大8倍)，相片上直徑=1/4毫米的圓圈，在底片上應是一個直徑為1/32毫 米的圓圈，這就是後來徠卡等照相機廠取模糊圈為1/30毫米的由來。

220px-Long_Short_Focus_1866

1866年模糊圈文章

 

走入術語的故鄉︰

Circle of confusion

In optics, a circle of confusion is an optical spot caused by a cone of light rays from a lens not coming to a perfect focus when imaging a point source. It is also known as disk of confusion, circle of indistinctness, blur circle, or blur spot.

In photography, the circle of confusion (CoC) is used to determine the depth of field, the part of an image that is acceptably sharp. A standard value of CoC is often associated with each image format, but the most appropriate value depends on visual acuity, viewing conditions, and the amount of enlargement. Properly, this is the maximum permissible circle of confusion, the circle of confusion diameter limit, or the circle of confusion criterion, but is often informally called simply the circle of confusion.

Real lenses do not focus all rays perfectly, so that even at best focus, a point is imaged as a spot rather than a point. The smallest such spot that a lens can produce is often referred to as the circle of least confusion.

Cirles_of_confusion_lens_diagram

The depth of field is the region where the CoC is less than the resolution of the human eye (or of the display medium).

Two uses

Two important uses of this term and concept need to be distinguished:

  1. For describing the largest blur spot that is indistinguishable from a point. A lens can precisely focus objects at only one distance; objects at other distances are defocused. Defocused object points are imaged as blur spots rather than points; the greater the distance an object is from the plane of focus, the greater the size of the blur spot. Such a blur spot has the same shape as the lens aperture, but for simplicity, is usually treated as if it were circular. In practice, objects at considerably different distances from the camera can still appear sharp (Ray 2000, 50); the range of object distances over which objects appear sharp is the depth of field (“DoF”). The common criterion for “acceptable sharpness” in the final image (e.g., print, projection screen, or electronic display) is that the blur spot be indistinguishable from a point.
  2. For describing the blur spot achieved by a lens, at its best focus or more generally. Recognizing that real lenses do not focus all rays perfectly under even the best conditions, the term circle of least confusion is often used for the smallest blur spot a lens can make (Ray 2002, 89), for example by picking a best focus position that makes a good compromise between the varying effective focal lengths of different lens zones due to spherical or other aberrations. The term circle of confusion is applied more generally, to the size of the out-of-focus spot to which a lens images an object point. Diffraction effects from wave optics and the finite aperture of a lens can be included in the circle of least confusion;[1] the more general circle of confusion for out-of-focus points is often computed in terms of pure ray (geometric) optics.[2]

In idealized ray optics, where rays are assumed to converge to a point when perfectly focused, the shape of a defocus blur spot from a lens with a circular aperture is a hard-edged circle of light. A more general blur spot has soft edges due to diffraction and aberrations (Stokseth 1969, 1317; Merklinger 1992, 45–46), and may be non-circular due to the aperture shape. Therefore, the diameter concept needs to be carefully defined in order to be meaningful. Suitable definitions often use the concept of encircled energy, the fraction of the total optical energy of the spot that is within the specified diameter. Values of the fraction (e.g., 80%, 90%) vary with application.

Adjusting the circle of confusion diameter for a lens’s DoF scale

The f-number determined from a lens DoF scale can be adjusted to reflect a CoC different from the one on which the DoF scale is based. It is shown in the Depth of field article that

{\mathrm {DoF}}={\frac {2Nc\left(m+1\right)}{m^{2}-\left({\frac {Nc}{f}}\right)^{2}}}\,,

where N is the lens f-number, c is the CoC, m is the magnification, and f is the lens focal length. Because the f-number and CoC occur only as the product Nc, an increase in one is equivalent to a corresponding decrease in the other, and vice versa. For example, if it is known that a lens DoF scale is based on a CoC of 0.035 mm, and the actual conditions require a CoC of 0.025 mm, the CoC must be decreased by a factor of 0.035 / 0.025 = 1.4; this can be accomplished by increasing the f-number determined from the DoF scale by the same factor, or about 1 stop, so the lens can simply be closed down 1 stop from the value indicated on the scale.

The same approach can usually be used with a DoF calculator on a view camera.

Circle_of_confusion_calculation_diagram.svg

Lens and ray diagram for calculating the circle of confusion diameter c for an out-of-focus subject at distance S2 when the camera is focused at S1. The auxiliary blur circle C in the object plane (dashed line) makes the calculation easier.

Determining a circle of confusion diameter from the object field

 

To calculate the diameter of the circle of confusion in the image plane for an out-of-focus subject, one method is to first calculate the diameter of the blur circle in a virtual image in the object plane, which is simply done using similar triangles, and then multiply by the magnification of the system, which is calculated with the help of the lens equation.

The blur circle, of diameter C, in the focused object plane at distance S1, is an unfocused virtual image of the object at distance S2 as shown in the diagram. It depends only on these distances and the aperture diameter A, via similar triangles, independent of the lens focal length:

C=A{|S_{2}-S_{1}| \over S_{2}}\,.

The circle of confusion in the image plane is obtained by multiplying by magnification m:

  c=Cm\,,

where the magnification m is given by the ratio of focus distances:

  m={f_{1} \over S_{1}}\,.

Using the lens equation we can solve for the auxiliary variable f1:

{1 \over f}={1 \over f_{1}}+{1 \over S_{1}}\,,

which yields

f_{1}={fS_{1} \over S_{1}-f}\,.

and express the magnification in terms of focused distance and focal length:

m={f \over S_{1}-f}\,,

which gives the final result:

c=A{|S_{2}-S_{1}| \over S_{2}}{f \over S_{1}-f}\,.

This can optionally be expressed in terms of the f-number N = f/A as:

c={|S_{2}-S_{1}| \over S_{2}}{f^{2} \over N(S_{1}-f)}\,.

This formula is exact for a simple paraxial thin lens or a symmetrical lens, in which the entrance pupil and exit pupil are both of diameter A. More complex lens designs with a non-unity pupil magnification will need a more complex analysis, as addressed in depth of field.

More generally, this approach leads to an exact paraxial result for all optical systems if A is the entrance pupil diameter, the subject distances are measured from the entrance pupil, and the magnification is known:

  c=Am{|S_{2}-S_{1}| \over S_{2}}\,.

If either the focus distance or the out-of-focus subject distance is infinite, the equations can be evaluated in the limit. For infinite focus distance:

  c={fA \over S_{2}}={f^{2} \over NS_{2}}\,.

And for the blur circle of an object at infinity when the focus distance is finite:

c={fA \over S_{1}-f}={f^{2} \over N(S_{1}-f)}\,.

If the c value is fixed as a circle of confusion diameter limit, either of these can be solved for subject distance to get the hyperfocal distance, with approximately equivalent results.

 

與概念對話，滌淨思慮吧☆