光的世界︰【□○閱讀】話眼睛《九》之附錄

2016-09-10 懸鉤子

術語因其目的而生，應其行業而別，所以在攝影天地裡講

超焦距

超焦距或稱 泛焦距離，攝影術語。是一個和焦距與光圈有關的對焦距離，當鏡頭以這個距離對焦時景深最大、可以從相機和對焦點之間的某處（景深前緣）起延伸到無限遠（景深後緣）。

從1933年開始，徠卡將超焦距尺刻印在鏡頭上，此後大部分各廠家出產的鏡頭或照相機，都有超焦距刻度。見圖一，將無窮遠對準箭頭(將鏡頭對焦在無窮遠),這時f8對準10米，這裡10米就是這個鏡頭在f8時的超焦距；用這枚鏡頭拍照，如將鏡頭對焦在無窮遠，用f8光圈，那麼從10米以外直到無窮遠的物體，在相片上保證清晰。如嫌景深不夠，可以收小光圈，例如用f16，則超焦距=5米，景深從5米到無窮遠。

SUMMICRON-HYPERFOCAL

徠卡SUMMICRON 50毫米鏡頭的超焦距

Hyperfocal distance

In optics and photography, hyperfocal distance is a distance beyond which all objects can be brought into an “acceptable” focus. There are two commonly used definitions of hyperfocal distance, leading to values that differ only slightly:

Definition 1: The hyperfocal distance is the closest distance at which a lens can be focused while keeping objects at infinity acceptably sharp. When the lens is focused at this distance, all objects at distances from half of the hyperfocal distance out to infinity will be acceptably sharp.

Definition 2: The hyperfocal distance is the distance beyond which all objects are acceptably sharp, for a lens focused at infinity.

The distinction between the two meanings is rarely made, since they have almost identical values. The value computed according to the first definition exceeds that from the second by just one focal length.

As the hyperfocal distance is the focus distance giving the maximum depth of field, it is the most desirable distance to set the focus of a fixed-focus camera.^[1]

。談可接受清晰度︰

Acceptable sharpness

The hyperfocal distance is entirely dependent upon what level of sharpness is considered to be acceptable. The criterion for the desired acceptable sharpness is specified through the circle of confusion (CoC) diameter limit. This criterion is the largest acceptable spot size diameter that an infinitesimal point is allowed to spread out to on the imaging medium (film, digital sensor, etc.).

Formulae

For the first definition,

H={\frac {f^{2}}{Nc}}+f

where

H

is hyperfocal distance

f

is focal length

N

is f-number (

f/D

for aperture diameter

D

)

c

is the circle of confusion limit

For any practical f-number, the added focal length is insignificant in comparison with the first term, so that

H\approx {\frac {f^{2}}{Nc}}

This formula is exact for the second definition, if H {\displaystyle H} $H$ is measured from a thin lens, or from the front principal plane of a complex lens; it is also exact for the first definition if $H$ is measured from a point that is one focal length in front of the front principal plane. For practical purposes, there is little difference between the first and second definitions.

從其推導

Derivation using geometric optics

The following derivations refer to the accompanying figures. For clarity, half the aperture and circle of confusion are indicated.^[2]

Accompanying figures

Definition 1

An object at distance H forms a sharp image at distance x (blue line). Here, objects at infinity have images with a circle of confusion indicated by the brown ellipse where the upper red ray through the focal point intersects the blue line.

First using similar triangles hatched in green,

{\begin{array}{crcl}&{\dfrac {x-f}{c/2}}&=&{\dfrac {f}{D/2}}\\\therefore &x-f&=&{\dfrac {cf}{D}}\\\therefore &x&=&f+{\dfrac {cf}{D}}\end{array}}

Then using similar triangles dotted in purple,

{\begin{array}{crclcl}&{\dfrac {H}{D/2}}&=&{\dfrac {x}{c/2}}\\\therefore &H&=&{\dfrac {Dx}{c}}&=&{\dfrac {D}{c}}{\Big (}f+{\dfrac {cf}{D}}{\Big )}\\&&=&{\dfrac {Df}{c}}+f&=&{\dfrac {f^{2}}{Nc}}+f\end{array}}

as found above.

Definition 2

Objects at infinity form sharp images at the focal length f (blue line). Here, an object at H forms an image with a circle of confusion indicated by the brown ellipse where the lower red ray converging to its sharp image intersects the blue line.

Using similar triangles shaded in yellow,

{\begin{array}{crclcl}&{\dfrac {H}{D/2}}&=&{\dfrac {f}{c/2}}\\\therefore &H&=&{\dfrac {Df}{c}}&=&{\dfrac {f^{2}}{Nc}}\end{array}}

可知是來自模糊圈的定義。若是對比著上篇所言︰

為什麼一張圖

一個式子

$c = A \frac{| S_2 - S_1 |}{S_2} \frac{f}{S_1 -f}$

$= \frac{| S_2 - S_1 |}{S_2} \frac{f^2}{N (S_1 -f)}$

這裡 $A = \frac{f}{N}$ 。

會令人如此困惑耶？假使不知道它說人眼『分辨率』有極限！藉此來定義『模糊』與『清晰』的分野。即使不談『孔徑』，一個透鏡也自有邊界 $A$ 的哩！更由於『成像條件』使得只有一物距 $S_1$ 能完美聚焦成像 $f_1$ 【像距】。就此而論其它 $S_2$ 遠、近之物在像面上將形成『彌散圓』，要是它小到人可將之視為『點』，此時視力不得不以為成像『清晰』的了。雖然那個式子貌似複雜，涉及多個參數，其中 $f$ 與 $N$ 是這個光學系統內稟參數，實際是以『聚焦之物』 $S_1$ ，論述『相對』它物 $S_2$ 所產生的『模糊圈』大小而已。在下面兩種情況裡， $c$ 得以簡化︰

【聚焦於無窮遠】 $S_1 \to \infty$

$c = \frac{f^2}{N S_2}$ ，與 $S_1$ 無關。

【相對無窮遠之物】 $S_2 \to \infty$

$c = \frac{f^2}{N (S_1 - f)}$ ，與 $S_2$ 無關。

或可先思其蘊涵意義耶！！

。第一定義以物在 $H$ 處之成像面 $x$ 為準，說相對無窮遠 $S_2 \to \infty$ 的它物所形成最大模糊圈是 $c$ ，因此 $H$ 之後之外的物體都能有一定的清晰渡 $\leq c$ 也。第二定義以聚焦於無窮遠處，講自無窮 $S_1 \to \infty$ 而來之近物 $H$ 在焦平面上所產生可接受彌散圓為 $c$ ，道理實相通矣。

若是已清楚明白清晰成像之判準，自能讀景深的推演了︰

Derivation of the DOF formulae

DOF for symmetrical lens.

DOF limits

A symmetrical lens is illustrated at right. The subject, at distance $s$ , is in focus at image distance $v$ . Point objects at distances $D_{{\mathrm F}}$ and $D_{{\mathrm N}}$ would be in focus at image distances $v_{{\mathrm F}}$ and $v_{{\mathrm N}}$ , respectively; at image distance $v$ , they are imaged as blur spots. The depth of field is controlled by the aperture stop diameter $d$ ; when the blur spot diameter is equal to the acceptable circle of confusion $c$ , the near and far limits of DOF are at $D_{{\mathrm N}}$ and $D_{{\mathrm F}}$ . From similar triangles,

{\frac {v_{{\mathrm N}}-v}{v_{{\mathrm N}}}}={\frac cd}

…………(1)

and

{\frac {v-v_{{\mathrm F}}}{v_{{\mathrm F}}}}={\frac cd}\,.

………..(2)

It usually is more convenient to work with the lens f-number than the aperture diameter; the f-number $N$ is related to the lens focal length $f$ and the aperture diameter $d$ by

N={\frac fd}\,;

…………………..(3)

The image distance $v$ is related to an object distance $s$ by the thin lens equation

{\frac 1s}+{\frac 1v}={\frac 1f}\,;

…………..(4)

${\frac {1}{D_{\mathrm {N} }}}+{\frac {1}{v_{\mathrm {N} }}}={\frac {1}{f}}$ ……….(5)

${\frac {1}{D_{\mathrm {F} }}}+{\frac {1}{v_{\mathrm {F} }}}={\frac {1}{f}}$ ……….(6)

Solve the equations set (1) to (6) and obtain the exact solutions without any simplification

D_{{{\mathrm N}}}={\frac {sf^{2}}{f^{2}+Nc(s-f)}}

………(7)

and

D_{\mathrm {F} }={\frac {sf^{2}}{f^{2}-Nc(s-f)}}\,.

……..(8)

Hyperfocal distance

Solving equation (8) for the focus distance $s$ and setting the far limit of DOF $D_{{{\mathrm F}}}$ to infinity gives

s=H={\frac {f^{2}}{Nc}}+f,

where $H$ is the hyperfocal distance. Setting the subject distance to the hyperfocal distance and solving for the near limit of DOF gives

D_{{{\mathrm N}}}={\frac {f^{2}/(Nc)+f}{2}}={\frac {H}{2}}\,.

Substituting the expression for hyperfocal distance into the formulas (7) and (8) for the near and far limits of DOF gives

$D_{\mathrm {N} }={\frac {s*(H-F)}{s+H-2*F}}$ …….(9)

$D_{\mathrm {F} }={\frac {s*(H-F)}{H-s}}$ …….(10)

For any practical value of $H$ , the focal length is negligible in comparison, so that

H\approx {\frac {f^{2}}{Nc}}\,.

Substituting the approximate expression for hyperfocal distance into the formulas for the near and far limits of DOF gives

D_{\mathrm {N} }\approx {\frac {Hs}{H+s}}

…….(11)

and

D_{\mathrm {F} }\approx {\frac {Hs}{H-s}}

……(12)

However, if one states by definition that $H={\frac {f^{2}}{Nc}}$ , then coming

D_{\mathrm {N} }={\frac {Hs}{H+(s-f)}}

and

D_{\mathrm {F} }={\frac {Hs}{H-(s-f)}}

Combining, the depth of field $D_{{{\mathrm F}}}-D_{{{\mathrm N}}}$ is

\mathrm {DOF} ={\frac {2Hs(s-f)}{H^{2}-(s-f)^{2}}}{\text{ for }}s<H{\text{ and }}H={\frac {f^{2}}{Nc}}\,.

也能旁通吧︰

Image-side relationships

Most discussions of DOF concentrate on the object side of the lens, but the formulas are simpler and the measurements usually easier to make on the image side. If the basic image-side equations

{\frac {v_{{\mathrm N}}-v}{v_{{\mathrm N}}}}={\frac {Nc}f}

and

{\frac {v-v_{{\mathrm F}}}{v_{{\mathrm F}}}}={\frac {Nc}f}

are combined and solved for the image distance $v$ , the result is

v={\frac {2v_{{{\mathrm N}}}v_{{{\mathrm F}}}}{v_{{{\mathrm N}}}+v_{{{\mathrm F}}}}}\,,

the harmonic mean of the near and far image distances. The basic image-side equations can also be combined and solved for $N$ , giving

N={\frac {f}{c}}{\frac {v_{{{\mathrm N}}}-v_{{{\mathrm F}}}}{v_{{{\mathrm N}}}+v_{{{\mathrm F}}}}}\,.

The image distances are measured from the camera’s image plane to the lens’s image nodal plane, which is not always easy to locate. The harmonic mean is always less than the arithmentic mean, but when the difference between the near and far image distances is reasonably small, the two means are close to equal, and focus can be set with sufficient accuracy using

v\approx {\frac {v_{{{\mathrm N}}}+v_{{{\mathrm F}}}}{2}}=v_{{{\mathrm F}}}+{\frac {v_{{{\mathrm N}}}-v_{{{\mathrm F}}}}{2}}\,.

This formula requires only the difference $v_{{{\mathrm N}}}\,-\,v_{{{\mathrm F}}}$ between the near and far image distances. View camera users often refer to this difference as the focus spread; it usually is measured on the bed or focusing rail. Focus is simply set to halfway between the near and far image distances.

Substituting $v_{{\mathrm N}}+v_{{\mathrm F}}=2v\,\!$ into the equation for $N$ and rearranging gives

N\approx {\frac fv}{\frac {v_{{{\mathrm N}}}-v_{{{\mathrm F}}}}{2c}}\,.

One variant of the thin-lens equation is $v=\left(m+1\right)f$ , where $m$ is the magnification; substituting this into the equation for $N$ gives

N\approx {\frac {1}{1+m}}{\frac {v_{{{\mathrm N}}}-v_{{{\mathrm F}}}}{2c}}\,.

At moderate-to-large subject distances, $m$ is small compared to unity, and the f-number can often be determined with sufficient accuracy using

N\approx {\frac {v_{{{\mathrm N}}}-v_{{{\mathrm F}}}}{2c}}\,.

For close-up photography, the magnification cannot be ignored, and the f-number should be determined using the first approximate formula.

As with the approximate formula for $v$ , the approximate formulas for $N$ require only the focus spread $v_{{{\mathrm N}}}\,-\,v_{{{\mathrm F}}}$ rather than the absolute image distances.

When the far limit of DOF is at infinity, $v_{{\mathrm F}}=f\,\!$ .

On manual-focus small- and medium-format lenses, the focus and f-number usually are determined using the lens DOF scales, which often are based on the approximate equations above.

將得拍照樂趣的乎☆

1280px-Jonquil_flowers_at_f5

At f/5.6, the flowers are isolated from the background.

樹莓派、樹莓派之學習、樹莓派之教育

光的世界︰【□○閱讀】話眼睛《九》

2016-09-09 懸鉤子

為什麼一張圖

一個式子

$c = A \frac{| S_2 - S_1 |}{S_2} \frac{f}{S_1 -f}$

$= \frac{| S_2 - S_1 |}{S_2} \frac{f^2}{N (S_1 -f)}$

這裡 $A = \frac{f}{N}$ 。

【聚焦於無窮遠】 $S_1 \to \infty$

$c = \frac{f^2}{N S_2}$ ，與 $S_1$ 無關。

【相對無窮遠之物】 $S_2 \to \infty$

$c = \frac{f^2}{N (S_1 - f)}$ ，與 $S_2$ 無關。

或可先思其蘊涵意義耶！！

Circle of confusion diameter limit in photography

In photography, the circle of confusion diameter limit (“CoC”) for the final image is often defined as the largest blur spot that will still be perceived by the human eye as a point.

With this definition, the CoC in the original image (the image on the film or electronic sensor) depends on three factors:

Visual acuity. For most people, the closest comfortable viewing distance, termed the near distance for distinct vision (Ray 2000, 52), is approximately 25 cm. At this distance, a person with good vision can usually distinguish an image resolution of 5 line pairs per millimeter (lp/mm), equivalent to a CoC of 0.2 mm in the final image.
Viewing conditions. If the final image is viewed at approximately 25 cm, a final-image CoC of 0.2 mm often is appropriate. A comfortable viewing distance is also one at which the angle of view is approximately 60° (Ray 2000, 52); at a distance of 25 cm, this corresponds to about 30 cm, approximately the diagonal of an 8″×10″ image. It often may be reasonable to assume that, for whole-image viewing, a final image larger than 8″×10″ will be viewed at a distance correspondingly greater than 25 cm, and for which a larger CoC may be acceptable; the original-image CoC is then the same as that determined from the standard final-image size and viewing distance. But if the larger final image will be viewed at the normal distance of 25 cm, a smaller original-image CoC will be needed to provide acceptable sharpness.
Enlargement from the original image to the final image. If there is no enlargement (e.g., a contact print of an 8×10 original image), the CoC for the original image is the same as that in the final image. But if, for example, the long dimension of a 35 mm original image is enlarged to 25 cm (10 inches), the enlargement is approximately 7×, and the CoC for the original image is 0.2 mm / 7, or 0.029 mm.

The common values for CoC may not be applicable if reproduction or viewing conditions differ significantly from those assumed in determining those values. If the original image will be given greater enlargement, or viewed at a closer distance, then a smaller CoC will be required. All three factors above are accommodated with this formula:

CoC (mm) = viewing distance (cm) / desired final-image resolution (lp/mm) for a 25 cm viewing distance / enlargement / 25

For example, to support a final-image resolution equivalent to 5 lp/mm for a 25 cm viewing distance when the anticipated viewing distance is 50 cm and the anticipated enlargement is 8:

CoC = 50 / 5 / 8 / 25 = 0.05 mm

Since the final-image size is not usually known at the time of taking a photograph, it is common to assume a standard size such as 25 cm width, along with a conventional final-image CoC of 0.2 mm, which is 1/1250 of the image width. Conventions in terms of the diagonal measure are also commonly used. The DoF computed using these conventions will need to be adjusted if the original image is cropped before enlarging to the final image size, or if the size and viewing assumptions are altered.

Using the “Zeiss formula”, the circle of confusion is sometimes calculated as d/1730 where d is the diagonal measure of the original image (the camera format). For full-frame 35 mm format (24 mm × 36 mm, 43 mm diagonal) this comes out to be 0.025 mm. A more widely used CoC is d/1500, or 0.029 mm for full-frame 35 mm format, which corresponds to resolving 5 lines per millimeter on a print of 30 cm diagonal. Values of 0.030 mm and 0.033 mm are also common for full-frame 35 mm format. For practical purposes, d/1730, a final-image CoC of 0.2 mm, and d/1500 give very similar results.

Criteria relating CoC to the lens focal length have also been used. Kodak (1972), 5) recommended 2 minutes of arc (the Snellen criterion of 30 cycles/degree for normal vision) for critical viewing, giving CoC ≈ f /1720, where f is the lens focal length. For a 50 mm lens on full-frame 35 mm format, this gave CoC ≈ 0.0291 mm. This criterion evidently assumed that a final image would be viewed at “perspective-correct” distance (i.e., the angle of view would be the same as that of the original image):

Viewing distance = focal length of taking lens × enlargement

However, images seldom are viewed at the “correct” distance; the viewer usually doesn’t know the focal length of the taking lens, and the “correct” distance may be uncomfortably short or long. Consequently, criteria based on lens focal length have generally given way to criteria (such as d/1500) related to the camera format.

If an image is viewed on a low-resolution display medium such as a computer monitor, the detectability of blur will be limited by the display medium rather than by human vision. For example, the optical blur will be more difficult to detect in an 8″×10″ image displayed on a computer monitor than in an 8″×10″ print of the same original image viewed at the same distance. If the image is to be viewed only on a low-resolution device, a larger CoC may be appropriate; however, if the image may also be viewed in a high-resolution medium such as a print, the criteria discussed above will govern.

Depth of field formulas derived from geometrical optics imply that any arbitrary DoF can be achieved by using a sufficiently small CoC. Because of diffraction, however, this isn’t quite true. Using a smaller CoC requires increasing the lens f-number to achieve the same DOF, and if the lens is stopped down sufficiently far, the reduction in defocus blur is offset by the increased blur from diffraction. See the Depth of field article for a more detailed discussion.

也可細想針孔成像之幾何光學原理果然太完美矣？？

每個『點光源』球狀各向發射光芒，獨有與『針孔』『成一線』者，方得入此間，因此光量小，故需『暗箱』護，否則難賭物，只因背景光線強。為何那『針孔』和『像面』之距離稱『焦距』？雖說『成一線』，實乃一『光錐』，匯聚在此處，術語不虛生，因襲稱『焦距』。有人還說『針孔相機』景深無限，深得廣漠無窮三昧︰

Depth_of_field_diagram

景深（英語：Depth of field, DOF）景深是指相機對焦點前後相對清晰的成像範圍。在光學中，尤其是錄影或是攝影，是一個描述在空間中，可以清楚成像的距離範圍。雖然透鏡只能夠將光聚到某一固定的距離，遠離此點則會逐漸模糊，但是在某一段特定的距離內，影像模糊的程度是肉眼無法察覺的，這段距離稱之為景深。當焦點設在超焦距處時，景深會從超焦距的一半延伸到無限遠，對一個固定的光圈值來說，這是最大的景深。

景深通常由物距、鏡頭焦距，以及鏡頭的光圈值所決定（相對於焦距的光圈大小）。除了在近距離時，一般來說景深是由物體的放大率以及透鏡的光圈值決定。固定光圈值時，增加放大率，不論是更靠近拍攝物或是使用長焦距的鏡頭，都會減少景深的距離；減少放大率時，則會增加景深。如果固定放大率時，增加光圈值（縮小光圈）則會增加景深；減小光圈值（增大光圈）則會減少景深。

對於某些影像，例如風景照，比較適合用較大的景深，然而在人像攝影時，則經常使用小景深來構圖，造成所謂背景虛化的效果。因為數位影像的進步，影像的銳利度可以由電腦後製而改變，因此也可以由後製的方式來改變景深。

─── 摘自《光的世界︰幾何光學二》

如是能得 $A = \frac{f}{N}$ 之意義乎？？！！

光圈對景深以及模糊圈的影響。焦點 (2) 可以在像平面 (5)成像，但是在不同距離的點，如（1 跟 3）則會投影出一個模糊的點，此點已大於模糊圈。減少光圈的大小 (4) 可以減小那些不在焦點上的點的模糊圈大小，因此模糊就變的比較不易察覺，看起來這些點就變成都在景深內

Depth of field

In optics, particularly as it relates to film and photography, depth of field (DOF), also called focus range or effective focus range, is the distance between the nearest and farthest objects in a scene that appear acceptably sharp in an image. Although a lens can precisely focus at only one distance at a time, the decrease in sharpness is gradual on each side of the focused distance, so that within the DOF, the unsharpness is imperceptible under normal viewing conditions.

In some cases, it may be desirable to have the entire image sharp, and a large DOF is appropriate. In other cases, a small DOF may be more effective, emphasizing the subject while de-emphasizing the foreground and background. In cinematography, a large DOF is often called deep focus, and a small DOF is often called shallow focus.

Summer_time_feet_in_Central_Park

The area within the depth of field appears sharp, while the areas beyond the depth of field appear blurry.

Circle of confusion criterion for depth of field

Precise focus is possible at only one distance; at that distance, a point object will produce a point image.^[1] At any other distance, a point object is defocused, and will produce a blur spot shaped like the aperture, which for the purpose of analysis is usually assumed to be circular. When this circular spot is sufficiently small, it is indistinguishable from a point, and appears to be in focus; it is rendered as “acceptably sharp”. The diameter of the circle increases with distance from the point of focus; the largest circle that is indistinguishable from a point is known as the acceptable circle of confusion, or informally, simply as the circle of confusion. The acceptable circle of confusion is influenced by visual acuity, viewing conditions, and the amount by which the image is enlarged (Ray 2000, 52–53). The increase of the circle diameter with defocus is gradual, so the limits of depth of field are not hard boundaries between sharp and unsharp.

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》

2016-09-08 懸鉤子

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:

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.
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.

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☆

樹莓派、樹莓派之學習、樹莓派之教育

光的世界︰【□○閱讀】話眼睛《七》

2016-09-07 懸鉤子

《采桑子》‧宋‧晏幾道

紅窗碧玉新名舊，
猶綰雙螺。
一寸秋波，
千斛明珠覺未多。

小來竹馬同遊客，
慣聽清歌。
今日蹉跎，
惱亂工夫暈翠蛾。

秋波明珠是何物？顧愷之畫人無阿堵！傳神寫照能勾魂攝魄，難怪耶靈魂衷情柏拉圖！！交子夢裡聞聲未睹，孔方得貝不識寶物︰

交子字憑號票生於宋太祖年間的四川，家道中落經營『交子鋪』維生，當時『千文鐵錢』重二十五斤，交易往來須用車拉錢十分不便，因得利於其名之故，成了個『私交子』，作著憑票兌換鐵錢的生意。閒暇之時，交子頗好古風喜讀文子《通玄真經》。文子是誰呢？文子姓辛號曰計然乃范蠡之師，學道早通是老子得意弟子，曾問學於子夏和墨子，若孔子見之必曰後生可畏。一日不知是『錢能通神』或是『書能通玄』，交子迷茫中見……

一人不識是何人，彷彿正問著另一人，也不識是何人？只聽得︰

老子曰：『有物混成，先天地生，惟象無形，窈窈冥冥，寂寥淡漠，不聞其聲，吾強為之名，字之曰道。』夫道者，高不可極，深不可測，苞裹天地，稟受無形，原流泏泏，沖而不盈，濁以靜之徐清，施之無窮，無所朝夕，表之不盈一握，約而能張，幽而能明，柔而能剛，含陰吐陽，而章三光；山以之高，淵以之深，獸以之走，鳥以之飛，麟以之遊，鳳以之翔，星曆以之行；以亡取存，以卑取尊，以退取先。古者三皇，得道之統，立於中央，神與化遊，以撫四方。是故能天運地墆，輪轉而無廢，水流而不止，與物終始。風興雲蒸，雷聲雨降，並應無窮，已雕已琢，還復於樸。無為為之而合乎生死，無為言之而通乎德，恬愉無矜而得乎和，有萬不同而便乎生。和陰陽，節四時，調五行，潤乎草木，浸乎金石，禽獸碩大，毫毛潤澤，鳥卵不敗，獸胎不殰，父無喪子之憂，兄無哭弟之哀，童子不孤，婦人不孀，虹蜺不見，盜賊不行，含德之所致也。大常之道，生物而不有，成化而不宰，萬物恃之而生，莫知其德，恃之而死，莫之能怨，收藏畜積而不加富，布施稟受而不益貧；忽兮怳兮，不可為象兮，怳兮忽兮，用不詘兮，窈兮冥兮，應化無形兮，遂兮通兮，不虛動兮，與剛柔卷舒兮，與陰陽俯仰兮。

，心想，這說的不就是文子的首篇《道原》嗎？，…

周失其道，五七后兮，勢水火兮，殷金夏貝，泉市之流，不識汝祖？問道方外耶！正想細聽，一陣喧嘩回過神來，已不復入夢矣，自此經常昏昏失魂悶悶落魄。

在繼續這個故事前，得先說著另一人，是與交子兩家通好為世交的孔方。孔方之祖發跡秦漢之際，歷數百代而至其父，其父因見家業衰敗想重振家風，故將其子命名孔方，深盼他能光宗耀祖。不想這孔方自幼狂狷性情尤喜清談玄風，雖然討厭自己的姓名，然而因為父命又不好改之，索性取字方地號天緣。由於師法王衍也愛『口中雌黃』，這王衍是誰？即以清談著稱的晉朝臨沂人王衍。他還流傳著一個故事︰

王衍的為人，說話每覺義理若有所不當時，就隨即改之，時人因而稱之口中雌黃 ── 經常用來修改錯字，古之修正液也 ──。他對結髮郭氏貪財性格非常不滿，所以從不說個錢字。郭氏因而刻意命婢女用錢圍住了床，王衍起床後不能走開，喚道︰『舉阿堵物卻！』。

。然而他雖師法王衍卻因出生其後，本想他該討厭這個阿堵一詞，卻因喜歡東晉顧愷之之畫而及於其詞。這個人說也奇怪畫人都不畫眼睛，他說：『傳神寫照，正在阿堵中。』，真不知是否阿堵 ── 眼睛 ── 果能勾魂攝魄。當日店裡來了一個客人拿來一物，孔方不識不知當不當買，因欲詢之而急尋交子。

─── 摘自《孔方之阿堵物》

既然老子曰︰有，名萬物之母。

道可道，非常道。名可名，非常名。無，名天地之始。有，名萬物之母。故常無，欲以觀其妙。常有，欲以觀其徼。此兩者同出而異名，同謂之玄。玄之又玄，眾妙之門。

辨物豈可不知名乎？？！！

角膜→房水【前室】→虹膜【瞳孔】→晶狀體→玻璃體【後部】→視網膜

囫圇者焉知其糊不糊塗！！？？

虹膜

虹膜又稱黃仁，眼睛構造的一部分，虹膜中心有一圓形開口，稱為瞳孔，猶如相機當中可調整大小的光圈，內含色素決定眼睛的顏色。日間光線較為強烈時，虹膜會收縮，只使一小束光線穿透瞳孔，進入眼睛；當進入黑暗環境中，虹膜就會往後退縮，使瞳孔變大，讓更多的光線進入眼睛，多數的脊椎動物的眼睛都有虹膜。因為每個人的虹膜都是不同的，所以也用於身份標識。

Menschliches_Auge

雙色虹膜與中央的黑色瞳孔

Iris (anatomy)

The iris (plural: irides or irises) is a thin, circular structure in the eye, responsible for controlling the diameter and size of the pupil and thus the amount of light reaching the retina. Eye color is defined by that of the iris. In optical terms, the pupil is the eye’s aperture, while the iris is the diaphragm that serves as the aperture stop.

250px-Human_Iris_JD052007

Iris is the blue area, with the pupil (the circular black spot) in its center, and surrounded by the white sclera. Overlying cornea is completely transparent so is not visible, except the high-gloss luster it gives the eye. Also pictured are the red blood vessels within the sclera. These structures are easily visible on any person’s eyes.

瞳孔

瞳孔又稱瞳神，是眼球血管膜的前部虹膜中心的圓孔。沿瞳孔環形排列的平滑肌叫瞳孔括約肌，收縮時使瞳孔縮小，沿瞳孔放射狀排列的平滑肌叫瞳孔放大肌，收縮時使瞳孔放大，調節進入眼球的光線量。因為內部吸收的關係，通常外觀呈黑色。

Iris.eye.225px

人眼近看。中間黑色的部分為瞳孔，周圍棕綠色部分為虹膜，外部白色部分為鞏膜。鞏膜中心最前面為透明的角膜。

動物的瞳孔

人類和很多動物（除了少數魚類）的瞳孔由不自覺的虹膜伸縮控制大小，以調節入眼內的光線強度。此稱為瞳孔反射。例如，人類瞳孔在強光下直徑大約1.5毫米，在暗淡光線中擴大到8毫米左右。

動物的瞳孔形狀由玻璃體的光學特性、視網膜的形狀和敏感度，以及物種的生存環境和需要決定。一般為圓形或縫狀，有些水生動物的瞳孔則有更奇異的形狀。

縫狀瞳孔常見於活動在不同光線強度下的動物。在強光下，這類瞳孔縮成細縫，然而仍然允許光線落到視網膜很大部分。開縫的方向可能與動物需要以高敏感度察覺的運動方向有關。例如家貓的瞳孔為豎立，便於察覺老鼠等獵物的橫向運動。很多蛇類也是縫狀瞳孔。

在用閃光燈照相的時候，瞳孔來不及及時關閉，閃光照亮眼底血管豐富的視網膜，形成紅眼現象。具有「防紅眼」功能的相機是預閃一次光，使瞳孔在正式閃光的時候已經達到收縮狀態。

Pupil

The pupil is a hole located in the centre of the iris of the eye that allows light to strike the retina.^[1] It appears black because light rays entering the pupil are either absorbed by the tissues inside the eye directly, or absorbed after diffuse reflections within the eye that mostly miss exiting the narrow pupil.

In humans the pupil is round, but other species, such as some cats, have vertical slit pupils, goats have horizontally oriented pupils, and some catfish have annular types.^[2] In optical terms, the anatomical pupil is the eye’s aperture and the iris is the aperture stop. The image of the pupil as seen from outside the eye is the entrance pupil, which does not exactly correspond to the location and size of the physical pupil because it is magnified by the cornea. On the inner edge lies a prominent structure, the collarette, marking the junction of the embryonic pupillary membrane covering the embryonic pupil.

250px-Eye_iris

The human eye
The pupil is the central transparent area (showing as black). The grey/blue area surrounding it is the iris. The white outer area is the sclera, the central transparent part of which is the cornea.

Controlling

The iris is a contractile structure, consisting mainly of smooth muscle, surrounding the pupil. Light enters the eye through the pupil, and the iris regulates the amount of light by controlling the size of the pupil. The iris contains two groups of smooth muscles; a circular group called the sphincter pupillae, and a radial group called the dilator pupillae. When the sphincter pupillae contract, the iris decreases or constricts the size of the pupil. The dilator pupillae, innervated by sympathetic nerves from the superior cervical ganglion, cause the pupil to dilate when they contract. These muscles are sometimes referred to as intrinsic eye muscles. The sensory pathway (rod or cone, bipolar, ganglion) is linked with its counterpart in the other eye by a partial crossover of each eye’s fibers. This causes the effect in one eye to carry over to the other. If the drug pilocarpine is administered, the pupils will constrict and accommodation is increased due to the parasympathetic action on the circular muscle fibers, conversely, atropine will cause paralysis of accommodation (cycloplegia) and dilation of the pupil.

Optic effects

When bright light is shone on the eye, light sensitive cells in the retina, including rod and cone photoreceptors and melanopsin ganglion cells, will send signals to the oculomotor nerve, specifically the parasympathetic part coming from the Edinger-Westphal nucleus, which terminates on the circular iris sphincter muscle. When this muscle contracts, it reduces the size of the pupil. This is the pupillary light reflex, which is an important test of brainstem function. Furthermore, the pupil will dilate if a person sees an object of interest.

The pupil gets wider in the dark but narrower in light. When narrow, the diameter is 2 to 4 millimeters. In the dark it will be the same at first, but will approach the maximum distance for a wide pupil 3 to 8 mm. In any human age group there is however considerable variation in maximal pupil size. For example, at the peak age of 15, the dark-adapted pupil can vary from 4 mm to 9 mm with different individuals. After 25 years of age the average pupil size decreases, though not at a steady rate.^[3]^[4] At this stage the pupils do not remain completely still, therefore may lead to oscillation, which may intensify and become known as hippus. The constriction of the pupil and near vision are closely tied. In bright light, the pupils constrict to prevent aberrations of light rays and thus attain their expected acuity; in the dark this is not necessary, so it is chiefly concerned with admitting sufficient light into the eye.^[5]

A condition called bene dilitatism occurs when the optic nerves are partially damaged. This condition is typified by chronically widened pupils due to the decreased ability of the optic nerves to respond to light. In normal lighting, people afflicted with this condition normally have dilated pupils, and bright lighting can cause pain. At the other end of the spectrum, people with this condition have trouble seeing in darkness. It is necessary for these people to be especially careful when driving at night due to their inability to see objects in their full perspective. This condition is not otherwise dangerous.

Diaphragm (optics)

In optics, a diaphragm is a thin opaque structure with an opening (aperture) at its center. The role of the diaphragm is to stop the passage of light, except for the light passing through the aperture. Thus it is also called a stop (an aperture stop, if it limits the brightness of light reaching the focal plane, or a field stop or flare stop for other uses of diaphragms in lenses). The diaphragm is placed in the light path of a lens or objective, and the size of the aperture regulates the amount of light that passes through the lens. The centre of the diaphragm’s aperture coincides with the optical axis of the lens system.

Most modern cameras use a type of adjustable diaphragm known as an iris diaphragm, and often referred to simply as an iris.

See the articles on aperture and f-number for the photographic effect and system of quantification of varying the opening in the diaphragm.

Iris_Diaphragm

Nine-blade iris

Aperture

In optics, an aperture is a hole or an opening through which light travels. More specifically, the aperture and focal length of an optical system determine the cone angle of a bundle of rays that come to a focus in the image plane. The aperture determines how collimated the admitted rays are, which is of great importance for the appearance at the image plane.^[2] If an aperture is narrow, then highly collimated rays are admitted, resulting in a sharp focus at the image plane. A wide aperture admits uncollimated rays, resulting in a sharp focus only for rays coming from a certain distance. This means that a wide aperture results in an image that is sharp for things at the correct distance. The aperture also determines how many of the incoming rays are actually admitted and thus how much light reaches the image plane (the narrower the aperture, the darker the image for a given exposure time). In the human eye, the pupil is the aperture.

An optical system typically has many openings, or structures that limit the ray bundles (ray bundles are also known as pencils of light). These structures may be the edge of a lens or mirror, or a ring or other fixture that holds an optical element in place, or may be a special element such as a diaphragm placed in the optical path to limit the light admitted by the system. In general, these structures are called stops, and the aperture stop is the stop that primarily determines the ray cone angle and brightness at the image point.

In some contexts, especially in photography and astronomy, aperture refers to the diameter of the aperture stop rather than the physical stop or the opening itself. For example, in a telescope the aperture stop is typically the edges of the objective lens or mirror (or of the mount that holds it). One then speaks of a telescope as having, for example, a 100 centimeter aperture. Note that the aperture stop is not necessarily the smallest stop in the system. Magnification and demagnification by lenses and other elements can cause a relatively large stop to be the aperture stop for the system. In astrophotography the aperture may be given as a linear measure (for example in inches or mm) or as the dimensionless ratio between that measure and the focal length. In other photography it is usually given as a ratio.

Sometimes stops and diaphragms are called apertures, even when they are not the aperture stop of the system.

The word aperture is also used in other contexts to indicate a system which blocks off light outside a certain region. In astronomy for example, a photometric aperture around a star usually corresponds to a circular window around the image of a star within which the light intensity is assumed.^[3]

Diagram of decreasing aperture sizes (increasing f-numbers) for “full stop” increments (factor of two aperture area per stop)

樹莓派、樹莓派之學習、樹莓派之教育

光的世界︰【□○閱讀】話眼睛《六》的拾遺

2016-09-06 懸鉤子

朱子語類‧論語十六

《志於道章》

問「志於道」。曰：「思量講究，持守踐履，皆是志。念念不舍，即是總說，須是有許多實事。」

吉甫說「志於道」處。曰：「『志於道』，不是只守箇空底見解。須是至誠懇惻，念念不忘。所謂道者，只是日用當然之理。事親必要孝，事君必要忠，以至事兄而弟，與朋友交而信，皆是道也。『志於道』者，正是謂志於此也。」

道理也是一箇有條理底物事，不是囫圇一物，如老莊所謂恍惚者。「志於道」，只是存心於所當為之理，而求至於所當為之地，非是欲將此心繫在一物之上也。

為何囫圇比恍惚呢，意指囫圇吞棗之囫圇乎？整個兒棗一口吞，豈能嚐出滋味耶！若說神志模糊謂恍惚，朱子囫圇一物講糊塗，心繫事理不二是常道，日用當然志實事。不過

只是存心於所當為之理，而求至於所當為之地，非是欲將此心繫在一物之上也。

之難難在難得關鍵處也︰

人類能夠『獨立思考』嗎？人們講︰因為他『如此說』，所以我『這般信』，難到這果是『合理』的嗎？？還是這真的『不合裡』的呢？？？就像有人探討後認為︰『差異』在『關鍵處』！也在『對的人』！！於是『問題』變成了是否『相信』了『對的人』，且在『事物』之『關鍵處』着力，就『這樣』……『決定』了……是否從此以後都能過著『自主判斷』的日子的了！！！

羅浮宮雕塑背後的標識符

一個『標識符』 ID identifier

能有多少好說之事，需要如是的陣仗？假使你已發現『身份證』比『你自己』更能『證明』你是誰！各種『號碼』效用之大，可以『轉帳購物』，你才剛知道『不變』 Immutable 之『物件』 object 要比『可變』 mutable 的『你』更『安全』『可靠』的哩！！不要『懷疑』，即使那些『號碼』因『你』而『有』，在『電腦語言』裡，他們可是『第一類公民』 First-class value ，享有第一等的『價值』？？

雖然有時令人『千迴百轉』的想不通？是『機器』服務於『人』，還是『人』符合『機器』的『處理』？！

或許那個『鄭三絕』能讓人們『回回神』的吧！『鄭板橋』固因『詩書畫』稱『三絕』，他傳聞軼事『也絕』︰

『絕對』難能卻『對』，
『絕句』自可斷『句』，
『絕情』反倒多『情』。

竹本【笨】虛心是我師

鄭板橋‧【一聯千金】

龍虎山中真宰相

麒麟閣上活神仙

【難得糊塗】

鄭縣令‧【崇仁‧大悲】寺‧庵之戀

硃筆一批

一半葫蘆一半瓢，合來一處好成桃；
徒令人定風歸寂，此後敲門月影遙：
鳥性悅時空即色，蓮花落處靜偏嬌；
是誰勾卻風流案，記取當年鄭板橋。

─── 摘自《W!o 的派生‧十日談之《六》》

所謂定律是經眾多事實支持方建立起來，然後形成理論體系，可以解釋現象原由，因此為『多之一』。談到定律應用則是從法則出發，符合各種條件，使得現象成真事物彰顯，亦是『多之一』的了！！不過這裡『理一』與『物一』也還是有分別的吧？？

理無大小、事無高低，原理觀物之法在能得義、用、通三昧而已。此處假借角膜焦距公式

$- \frac{1}{f} = \frac{N_f - N_{out}}{N_{out} R_{out}} + \frac{ - N_f + N_{in}}{N_{out} R_{in}} + \frac{(- N_f + N_{in}) t (N_f - N_{out})}{N_{out} N_f R_{in} R_{out}}$

說說這個方法。先將此式依造透鏡者方程式形制改寫如下

$\frac{N_{out}}{f} = \frac{N_f - N_{in}}{R_{in}} - \frac{N_f - N_{out}}{R_{out}} + \frac{(N_f - N_{in}) (N_f - N_{out}) t}{N_f R_{in} R_{out}}$

假如

【 $N_f = N_{in}$ 】

$\frac{N_{out}}{f} = - \frac{N_f - N_{out}}{R_{out}}$

只剩後面乎！

或

【 $N_f = N_{out}$ 】

$\frac{N_{out}}{f} = \frac{N_f - N_{in}}{R_{in}}$

唯有前面耶？

此事奇怪嗎？且問相同折射率之介質間能有折射耶？或可發生反射乎！若無作用怎講厚度 $t$ 的哩！！

其次按造角膜主平面成像條件

$\frac{N_{in}}{D_{in}} + \frac{N_{out}}{I_{out}} = \frac{N_{out}}{f}$

當

【 $N_{in} = N_{out}$ 】時，自然化作

$\frac{1}{D_{in}} + \frac{1}{I_{out}} = \frac{1}{f}$

豈不正常嘛？？

那麼如果已知水的折射率為 $1.333$ ，角膜的折射率為 $1.376$ ，房水的折射率為 $1.336$ ，能否用於了解

潛水面鏡

潛水面鏡（英語：Diving mask，又稱：dive mask或scuba mask），通稱潛水鏡，是潛水裝備的一種，可以讓水肺潛水員、自由潛水員及浮潛人士能夠清楚地看到水底的東西^[1]。當人類眼睛與水直接接觸時，光的折射角度會與空氣中略有不同，導致眼珠無法聚焦，影像變得模糊不清，潛水面鏡與眼睛之間的空氣正好解決了這個問題。

Diving mask

A diving mask (also half mask, dive mask or scuba mask) is an item of diving equipment that allows underwater divers, including, scuba divers, free-divers, and snorkelers to see clearly underwater.^[1]^[2] Surface supplied divers usually use a full face mask or diving helmet, but in some systems the half mask may be used.^[2] When the human eye is in direct contact with water as opposed to air, its normal environment, light entering the eye is refracted by a different angle and the eye is unable to focus the light. By providing an air space in front of the eyes, light enters normally and the eye is able to focus correctly.

的設計原理，真的只需存在『空氣隙』，視覺就能恢復了嗎？？？反思此時 $f$ 因為有『空氣‧角膜』之界面終將如何計算的呢！！！將可通讀水中光學產品科技文字矣☆☆

FreeSandal

每月彙整: 2016 年 9 月

光的世界︰【□○閱讀】話眼睛《九》之附錄

超焦距

Hyperfocal distance

Acceptable sharpness

Formulae

Derivation using geometric optics

Definition 1

Definition 2

Derivation of the DOF formulae

DOF limits

Hyperfocal distance

Image-side relationships

光的世界︰【□○閱讀】話眼睛《九》

Circle of confusion diameter limit in photography

Depth of field

Circle of confusion criterion for depth of field

光的世界︰【□○閱讀】話眼睛《八》

模糊圈

Circle of confusion

Two uses

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

Determining a circle of confusion diameter from the object field

光的世界︰【□○閱讀】話眼睛《七》

虹膜

Iris (anatomy)

瞳孔

動物的瞳孔

Pupil

Controlling

Optic effects

Diaphragm (optics)

Aperture

光的世界︰【□○閱讀】話眼睛《六》的拾遺

潛水面鏡

Diving mask

輕。鬆。學。部落客

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