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20100606

超焦距及其應用(續)

The Physical Theory of Hyperfocal Distance and its Application to Photography (cont.)

May, 2010

Ringo Cheung

Abstract
Last time the hyperfocal distance equation in terms of f, N and c was derived from the thin lens formulas. In this article, the relationship between H with f, N and c will be analyzed and some physical inference will be discussed.

Relationship of H with f
Recall that the equation for hyperfocal distance H is given by :

Since H varies with the square of f rather than linearly, a small increase in f will result in a large increase in H. For example, for a 25mm lens of 135 format, H = 2.72m at an aperture of F8; while that for a 50mm lens, H = 10.83m at the same F-stop.

Graph of H vs. f
The 2nd time derivative of H w.r.t. f is :

and the minimum of H exists at f = -Nc/2, the graph concaves upwards. By considering only positive values of f for practical purposes, the graph of H vs. f for 135mm format camera (coc = 0.029) and an F-stop of N = 8 is :

For focal length of 35mm and longer, H is over 5.32m. While this is useful for scene photography, it is not very convenient for street photography and snapshot.

Graph of H vs. N
For a lens of fixed f and c, H is strictly decreasing with N since

as c > 0. On the other hand, a larger f-number means a smaller aperture. Therefore a larger f-number like f8 or f11 will result in a smaller H than with f4. The graph of a 25mm lens (135 format, i.e. coc = 0.029) with f-number from 1 to 16 is depicted below :

which is a hyperbola.

Relationship of H vs. c
Roughly speaking, H is strictly decreasing with c from the hyperfocal distance equation. However, since cameras of different formats have their own definition of wide angle, standard and telephoto lenses, (e.g. a standard 50mm lens in 135 format is considered a wide angle lens in 6x6, 120 format, with c = 0.053) a direct comparison of H vs. c (i.e. different camera formats / film sizes) is not of much practical usefulness.

Conclusion
From the above discussion, a wide angle lens set at small aperture (i.e. a large f-number) is a good candidate for short hyperfocal distance (H) and is more convenient for street and snapshot photos.

20091025

The Physical Theory of Hyperfocal Distance and its Application to Photography

The Physical Theory of Hyperfocal Distance and its Application to Photography

Ringo Cheung

Oct, 2009

Introduction

Applying the method of producing a long depth of field has long been the practice of experienced photographers, especially for those who are engaged in scene photography. Ansel Adams, who is widely recognized as the master of large format natural scene photography and dark room expert, established the "Group f/64" [1] with some other experts like Edward Weston in the same field. It is known that with a smaller aperture of lens (i.e. larger f-number), a longer (larger) depth of field can be achieved. While this is a widely accepted general knowledge among the professionals and even serious amateurs, the concept and application of Hyperfocal Distance (HFD), which extends the depth of field to a distance of infinity, was largely ignored by modern photographers. This can be seen from the lack of "depth of field" indicator in some modern lenses manufactured today [2].

In this article, important concepts that lead to HFD such as lens maker formula, circle of confusion (COC) and depth of field (DOF) will be explained. It is then followed by an explanation of how the equation of HFD is derived. Finally, its applications to photography will be explained with examples.

Circle of Confusion (COC) and Depth of Field (DOF)

The concept of COC is highly related to depth of field (DOF). Due to the defects of human eyes, we are not able to distinguish a very small circle from a very small spot [3]. When a cone of light rays passes through a lens, it is not perfectly focused even when imaging a point source, instead, an optical spot is resulted. This is the COC, and is used to determine the DOF, the part of the image that is acceptably sharp. Different lens manufacturers have different values of COC. The widely accepted values of COC for 35mm format is 0.03mm, for APS format is 0.02mm and for Four Thirds System is 0.015mm [4].

Hence, DOF can be viewed as the portion of the scene that is acceptably sharp, or appears to be sharp in the image. In some images such as landscape or scene photography, a large DOF is desirable, or appropriate, to depict the fine details of the scene. As a result, scene photographers usually use a very small aperture to achieve a long DOF.

Largest DOF is achieved when focus is set to the so called HFD. The DOF will extend from half the HFD to infinity (as will be proved below). This is the largest DOF possible for a given f-number.

Hyperfocal Distance (HFD)

The following discussion assumes the use of symmetrical thin lenses. For asymmetrical lenses, a factor called "pupil of magnification" must be taken into consideration [5].

Fig.1

Referring to Fig.1 and making use of similar triangles and the thin lens equation [6]

where as usual, O is the object distance, I is the image distance and f the focal length, the near and far limits of DOF is given by [5]:

and

where

s is the subject distance

f is the focal length of the lens

N is the aperture

c is the COC

The HFD formula is derived as follow. According to the definition of HFD, the far limit of DOF, DF is infinity. Hence the denominator vanishes, giving:

where H is the HFD.

On the other hand, the near limit or DN will be H since we are focusing on the HFD. Setting s to H and solving for DN gives [5]:

Hence the depth of field will extend from half of the HFD to infinity.

Examples of Applications of HFD

Recall the formula for HFD is

For a 35mm format camera with typical COC value of 0.03mm, using an f-number of f16 and a lens of focal length 50mm, the HFD is

H = (50)2/ (16 x 0.03) + 50 = 5258.33mm≒5.26m

Hence for this lens using an aperture of f16 and focusing on a distance of 5.26m, the DOF will extend from approximately 5.26÷2 = 2.63m to infinity.

Fig.2

To set the HFD on the camera, first adjust an f-number that will be used, e.g. f16. Then on the lens DOF indicator, set the focus to infinity (fig. 2) [7]. We can see that the DOF indicator gives us the DOF from approx. 5m to infinity. Then turn the focusing ring on the lens until it focuses on the hyperfocal distance of 5m (fig. 3). Now the DOF will be from 2.5m to infinity, meaning that anything within this range will be sharp. In other words, HFD maximizes usable DOF.
With appropriate use of the HFD theory, snap shot on the street (aka street photography) would become easy. By estimating the hyperfocal distance, everything within the range will be sharp. Photographers need only concentrate on framing and motion of the subjects, instead of worrying about the sharpness [7].

References

[1] Biography of Ansel Adams, The Ansel Adams Gallery - http://www.anseladams.com/content/ansel_info/anseladams_biography2.html
[2] DOF, Hyperfocal distance and Calculator, Guides @ nikonians.org - http://www.nikonians.org/html/resources/guides/dof/hyperfocal4.html
[3] 高品質黑白攝影的技法, 蔣載榮, 雄獅圖書股份有限公司, 1996, p.20
[4] Circle of confusion, Wikipedia - http://en.wikipedia.org/wiki/Circle_of_confusion
[5] Depth of field, Wikipedia - http://en.wikipedia.org/wiki/Depth_of_field
[6] How to derive the thin lens equation, Hirophysics.com - http://hirophysics.com/Anime/thinlenseq.html
[7] Using Hyperfocal Distance in Street Photography, Olympus/Zuiko - http://olympuszuiko.wordpress.com/2007/03/20/using-hyperfocal-distance-in-street-photography/

20070721

攝影人必須是獨行俠

當然，不是所有玩攝影的人也是獨行俠，不然香港便沒有那麼多攝影(學)會了。

伍振榮的『攝影獨白』裡面提過，一班人的攝影活動，美其名是大家一起研究影藝，其實都不過是一些『聯誼活動』罷了。

我對這點絕對身同感受，而且由初學攝影開始到之後的幾年都曾經歷過。尤其在工聯會的歲月，在外影的日子，幾部大旅遊巴士一同出發，到新界的拍攝景點『苦練』影技。那種人頭湧湧的盛況，仿佛眼前就是香港五六十年代攝影的黃金歲月。

我不是一個很 social 的人，所以到場後，都會聆聽導師的指導，然後開始拍攝。最初是他叫我們拍什麼便拍什麼。後來自己進步了，拍完『功課』後，便獨個兒走開，找些花草樹木來拍。

當中總會有些人做別的東西，例如三五成群閒聊，情侶拍拖，結識異性等等。

但最令我反感的，莫過於一幕幕『晒器材』的場面。

同學中總會有些帶著昂貴而先進器材的達官貴人，在我身邊走過，有時他們不是真的要拍，只是『晒晒』他們的 Leica 或 Nikon F4，F5 而已。

更甚者，三五知己圍在一起，先是一人高談闊論，大談自己的器材有多先進，過片(即連環快拍時每秒可以過幾多張底片，那時還是菲林時代)有多快多快，鏡頭光圈有幾大幾大等等。然後通常是有幾個人附和的笑聲，當中可能還夾雜著羨慕的眼神。

之後會愈吹愈遠，又大談自己的經歷，或者在哪裡見過更強更大的器材等等。

最初聽在耳裡，當攝影界的新聞來理解一下，增廣見識，倒也沒什麼。但久而久之聽得多了，開始有些反感。

攝影是門藝術，或者低檔一點來說，是門手藝。所以，和『技術』的關係一定較『器材』為密切。每次在拍攝的景點聽到一大班人不思進取地大談自己收藏器材之道，如數家珍，總會想：為什麼不談談『慢快門閃燈同步』、『什麼叫倒逆率失效』、『如何可以達到超焦距』、『攝影家的 f16 定律』、『何時需要使用中灰漸變濾光鏡』......等等，一大堆的技術問題？

今日在坊間買到的所謂數碼攝影攻略書，翻開一看，裡面介紹的一大部份數碼攝影的技術問題，其實都是上述那些。可見縱使時代不同，器材相異，要解決的技術問題，其實還是那一大堆老問題。所不同者，多了個後期的 PS CS3 而已。

當然，你又會說：『工欲善其事，必先利其器。』

那請留意，你要『學』攝影的話，任何一部最基本的，可更換鏡頭的單鏡反光相機，那怕只有光圈快門，已自足用。

『這張相裡面的眼睛夠 sharp 吧？當然還未夠。但如果拍攝人像，永遠也只講求張相是否夠 sharp，那我看大可不必再學攝影了，只需有錢買昂貴器材，便張張是佳作，人人變大師！』

可見這個群體的學習階段，有很多誘惑(即毒害你去買新器材的人)，更有不少剝奪你學習時間的東西。這不僅是指 official 的攝影班活動，就連三五知己出來拍風景，影 model，也都不可避免淪為『聯誼俱樂部』。數碼攝影年代，除了晒攝影器材，還可以晒記憶卡，晒 MP4 Player，晒手提電腦！

至於模特兒拍攝，那怕只是五、六個攝影師，但由於面形、光線和姿勢的問題，『好位』通常只有一兩個，除了要排隊拍攝之外(如果秩序真的如此良好的話)，還要看你夠不夠『惡』和『狠』。

事緣有些影友很奇怪，對於如何教 model 擺 pose，在哪個位置拍攝，有什麼 idea 等等，全無頭緒，就是不停在等運到。每當你有 idea ，剛剛指導完 model 應如何擺姿勢，而自己舉起相機開始構圖拍攝時，那群等運到的人便一擁而上，搶拍！

當然他們有自己的美學觀念，構圖亦各施各法，這個我不願置評。但可否對提出這個 idea 的人尊重一點，讓他來先拍？

更『攞命』的，是當原創人(在這個案中是我自己)真的要按下快門時，忽然有另一個人走過來，大聲問道：『Ringo 你影完未？』意即他要帶 model 到另一個位置了。

香港攝影的黃金時代一去不復返，不無道理。如此未經心思熟慮便猛按快門狂拍，除了製造更多垃圾影像外，我再看不出有什麼好的 side effect 了。

如果他們這些快鎗手是拍 jpeg，那還可以。如果用 raw file (每張十幾 MB)，那我要恭喜他們了。曾經在一個人像攝影班的外影活動裡，見過有一位同學用四、五張的連還快拍設定，每次按快門時，大家就會聽到機關槍式的『啪啪啪啪啪！』如果將他的攝影作品用每秒廿四格來播放，真可以變成一套電影！

記憶卡和電腦硬碟在一些人的心目中真的可以賤價到如此地步，你都咪話唔驚！

我在此強烈建議：所有稍為有丁點兒上進心的攝影人，『聯誼活動』，可免則免。尤其是那些電腦相機電玩展裡拍攝 IT 女郎、車展女郎、cosplay、室內冷氣開放永遠用世界光打燈的女像攝影活動 ...... 等等。我敢保證，以上這些活動，任你再參加多十年，你的影技也不會有絲毫進步！

攝影是要思考的，攝影人，還是做獨行俠好！

20070612

攝影中的八字真言

很多年以前，當我剛剛開始學攝影不久，有個不懂攝影的舊同學問我，怎樣才算是一張相。那時候我的答案很簡單：有主體的，便算是一張相了。

當然，隨著影齡日增，這個答案有需要修改一下。

首先，就視覺訊息傳遞有效與否這個問題來說，單是有主體的相(或影像)是不一定足以令觀眾產生共鳴的。這個主體必須是突出的，是鮮明的，要讓人一眼便看得出這張相想表達的是什麼。

大約十年前，我和幾個朋友一起上過一位攝影界老前輩的攝影班。由初級黑房技術和初級攝影學起，一真到高級斑，再到深造班。雖然課程內容五花八門，可以說，我們由最基本的學起，然後慢慢遞進，一直到我相信是幾乎所有拍攝情況也涵蓋了，到了極度鑽牛角尖的地步，但是，對於在如何影得一張好相這個問題上，老師常常強調，只有八字真言，就是：『背景統一，主體突出』。

這位老師出過幾本有關黑房技術(是真正用菲林來沖晒放的黑房技術，不是 Photoshop)的書，一般被影友視為『寶典』。但記憶中，關於攝影的教材，就只出過一本『攝影取景術』。

這本教人如何拍攝『攞景』的教材，我認為是同類教材之中的極品。除了由始至終也貫徹以上所說的八字真言之外，每一章裡面說的關於取景的克難過程，直教人心悅誠服，茅塞頓開。這類教材書，外國和台灣出版的也有不少。但總覺得它們有點隔著靴搔癢的感覺，其一是太快到達終點，由第一張相開始就已是色彩艷麗的名山大川，把觀眾的視線也轉移了；又或者只談景物之間的配合問題，橫影還是直影，地平線和天空的比例要如何等等。根本甚少分析攝影師應要如何走位，如何等待時機等等最關鍵的問題。

反觀『取景術』一書所談的，很多都是如何由到達拍攝場地，看見一個『爛景』而毫無頭緒開始，由辨認出主體，通過一系列的觀察和走位，包括改變距離和角度等等，直到使主體能夠位於最有利、最突出的位置為止。當中可能會經過放棄某一拍攝位置的過程，書裡面也會解釋得一清二楚。這種讓讀者能夠像跟攝影師一起去經歷一個個拍攝過程的圖文並茂的 present 手法，其他同類的教材是很少見的。

當然，我今天對『怎樣才算是一張相』這個問題，除了『主體』之外，還有『主題』呢。但這種『每一張相背後都有一個故事』的問題，則比單純的『主體』來得更有深度，是另一個課題了。

數碼時代的今天，當人人手中的記憶卡是4GB或8GB的時候，每張相的成本也大大地降低了。但隨之而來的濫拍現象卻日益增加。究竟大家在按下快門之前的一剎那，有否想過去苦心經營一張傑作？還是在家中的硬碟裡不停製造垃圾影像、垃圾資訊？