每日彙整: 2016-09-23

樹莓派、樹莓派之學習、樹莓派之教育

光的世界︰【□○閱讀】樹莓派近攝鏡‧中

知道一個公式

New closest point = \frac{x}{D x + 1}

，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。

120px-80a_tungstene_f

 

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]

300px-board_lens

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︰

630_g_1461887471464

 

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）。

220px-achromat_doublet_en-svg

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]

OLYMPUS DIGITAL CAMERA

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！！？？

 

close-up

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 f_{ob.} 的相機，由於感光膠卷、CCD  或 CMOS 之成像位置 X_{img} 也是固定的。假設以等效主平面之薄透鏡成像條件︰

\frac{1}{X} + \frac{1}{X_{img}} = \frac{1}{f_{ob.}}

來作考察，唯有一個物距 X 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 X_{HypF} 之物距︰

\frac{1}{X_{HypF}} + \frac{1}{X_{img}} = \frac{1}{f_{ob.}}

，以得 \frac{X_{HypF}}{2} 到 \infty 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 X \to \infty ， 此時成像面 X_{img} 就是 焦距面︰

\frac{1}{\infty} + \frac{1}{X_{img}} = \frac{1}{f_{ob.}}

\therefore X_{img} = f_{ob.} = f 。

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:

  X_{{\text{max}}}=1/D

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 f_{c-up.} = \frac{1}{D} 與相機鏡頭緊貼，組合系統可以用等效薄透鏡 f_{eq.} 來描述︰

\frac{1}{f_{eq.}} = \frac{1}{f_{ob.}} + \frac{1}{f_{c-up.}} 。

當其它條件維持不變，此時能夠完美成像織物距 X_{max} 將滿足︰

\frac{1}{X_{max}} + \frac{1}{X_{img}} = \frac{1}{f_{eq.}}

\therefore \frac{1}{X_{max}} = \frac{1}{f_{eq.}} - \frac{1}{X_{img}}

= \frac{1}{f_{ob.}} + \frac{1}{f_{c-up.}} - \frac{1}{f_{ob.}}

= \frac{1}{f_{c-up.}} = D 。

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:

  M_{{\text{Xmax}}}=fD

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 M_{X_{max}}

= \frac{X_{img}}{X_{max}} = f D 。

為什麼要稱之為 X_{max} 的呢？這可由底下類似的推導，當 X \to \infty 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_{{\text{min}}}=X/(DX+1)

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

\frac{1}{X} + \frac{1}{X_{img}} = \frac{1}{f_{ob.}} \ (1)

\frac{1}{X_{min}} + \frac{1}{X_{img}} = \frac{1}{f_{eq.}} \ (2)

而且 \frac{1}{f_{eq.}} = \frac{1}{f_{ob.}} + \frac{1}{f_{c-up.}} 。從 (2) -(1) ，解之得

X_{min} = \frac{X}{D X + 1} 。所以

\lim \limits_{X \to \infty} X_{min} = \frac{1}{D} = X_{max} 。

 

如果讀者明白

M_{X_{min} \cdot X_{min} = M_X \cdot X = X_{img} ，

了解

\lim \limits_{X \to \infty} X_{img} = f_{ob.} 。

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_{{\text{Xmin}}}=M_{{\text{X}}}(DX+1)

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

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

It is at this Xmin 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.