[推荐]『徕卡设计师谈镜头设计』

华山老妖 · 发表于 2003-9-24 18:53:00

  镜头设计的第一步是拟出规格表，内容包括对新镜头的要求及
其特性，如镜头的焦距、光圈及允许的渐晕系数。基于这些数据，设
计师构建一个”初始系统”或称”基本系统”以便进一步加以优化。
该系统已经满足了镜头设计规定的要求，但在成保质量方面仍存在
缺陷。设计新镜头时，数学模型也可以作为初始系统。
  设计师的第二步工作是修正系统中存在的像差。有几种可能的
方法来校正保差，视设计师经验而不同。一次性校正好所有像差几
乎是不可能的。通常，设计师会选择几种主要像差先行校正，其结
果有两种可能：一是总体成像质量提高了．但出现了新的像差或原
有的非主要像差成为主要像差。此时，他会重新选择主要像差继续
校正，经过多次校正直至达到规定的要求；另一种可能是：像差无
法校正，此时，设计师别无选择，只能把原有的初始系统推翻，选
择新的初始系统重新开始。
  除了成像质量．优化过程中还要考虑其它因素，包括逆光时反
射的发生机率、耀斑的发生机率和制造的允许公差，特别是最后一
项，设计中经常出现图像质量很好、但制造公差过于严格，以至于
制造成本过高或根本无法制造的情况。此时优化过程无法继续，只
能推倒重来。
  让我们用一个实例来说明镜头的设计过程。一个最普通135相机
用的50毫米f／2苏米克隆标准镜头的设计资科也有数百页，为简化
起见．我们用一个假定的画面对角线长度为24毫米的50毫米f／5．6
镜头为例来说明镜头的设计步骤(35毫米相机画面对角线实际长度
为43．2毫米)。首先，我们用一个很小的像点来检验镜头的还原性，
以此为标准来评价优化过程每一步的结果。当然，实际的图像比一
个像点要复杂得多，但任意一个图像都是由无数个这样的小像点组
成的(就像报纸上组成文字的一个个小墨点或数字位固中的像素一
样)，如果单独一个保点不能准确地还原，那么从理论上讲，整个
图像也不能准确地还原。为此，我们在下文中用一个像点的表现来
代替整个图像的表现。
  第一步：建立初姑系统(或称基本系统)
  基于数学原因，对于规格中每一个特定的要求(包括像差值)
至少应有一个自由变量，这一点很重要。”自由变量”一词在光学
设计上指的是特定的焦距、每块玻璃镜片的表面曲率和物理特性。
不是所有的输入变量对镜头的物理特性都会产生影响的。比如，镜
头玻璃的色散系数就不会影响镜头的焦距。因此，校正镜头的色差
时，镜头玻璃的色散系数是最适合的自由变量。
  在一个影像圈直径24毫米、光圈f／5．6的光学系统中，校正8个
主要的像差就可以了。进一步的要求还包括镜头的焦距、系统总的
构建长度和最后一片镜片与成保平面之间的距离3项，所以共有11
项要求。在另一方面，每片镜片中有5个变量是有效的：镜片的两
个半径、镜片的轴向厚度、玻璃的折射系数和色散系数。为达到镜
头设计要求，至少需要3片镜片，图1是初始系统的剖面团。每片镜
片的焦距经过精心选择，以使系统总焦距为50毫米；每片镜片的直
径决定于镜头的光圈和允许的渐晕；而对每片镜片的实际形状和使
用的玻璃类型却没有特殊要求，因此我们把它作为”自由变量”。
  在图1中我们可以看到，不是所有的光线都会聚在成像平面的
同一个点上，即存在看像差。图2显示了一个像点的相关像差：上
图显示的是图像边缘的像差；中国显示的是图像边缘和中间之间的
保差；下图显示的是图像中间的像差。
  第二步：校正图像中间像差
  通常，设计师会先校正图像中心的保差，方法是改变3片透镜
的曲率，通过巧妙的组合达到既校正中心像差又减小边缘像差的目
的。这里用改变曲率的方法来校正像差的好处是；它只改变像差而
不影响镜头的焦距。为达到最佳的校正效果，需要同时改变3个透
镜的曲率。因为如果只改变最后一片透镜的曲率，画面中央的像差
可能被校正了，但边缘的像差会变大(见图3)；如果只改变第一或
第二片透镜的曲率，也会有类似的结果。最好的结果是图4，中央
和边缘的像差都得到了校正。
  第三步：校正图像边缘像差
  为了校正图像边缘的像差，仍然用曲率作为自由变量就不适用
了，应重新选择另一种变星。此时，设计师可以从透镜的折射率和
轴向厚度中选择一种作为自由变量。在这个例子中．用折射串作自由变量特别合适。因为在这个这个系统中，折射宰决定了光线在透
过玻璃与空气的界面时被折射(或弯曲)的程度。折射率越高，光
线被折射的程度就越大。经过大量的排列组合试验．设计师得到了
国5所示的最佳结果。
  第四步：校正色差
  到目前为止．我们只考虑了对绿光下像点像差的校正。而实际
上，透镜对红光、蓝光和绿光的折射率是不同的．因此．我们必须考
虑对像点进行不同色光下的色差校正。图6给出了同一像点在蓝光．
红光和绿光下的不同色差情况。色差可以用改变透镜的色散系数来控
制．通过巧妙地选择玻璃类型，色差几乎可以被完全消除，但要确保
透镜的折射率不再改变。这一步骤的结果显示在图7上。从图上可以
看出：像点非常小，对比度仍然很高‘但边缘部分略有下降。
  第五步：检查加工公差和耀斑情况
  镜头设计的最后一步是检查加工公差是否合适和耀斑情况是否
严重。这一步相对简单，但如果加工公差过严或耀斑情况严重，以
前的全部工作就功亏一窑了。
  图8是最后完成的镜头光路图。与图1的镜头光路图相比
起来差别不大，但实际上成像质量有了很大的提高。
  需要说明的是，我们上面举例介绍的是一个大大简化的光学系
统。目的是更清楚地向大家介绍镜头设计的基本步骤。实际的设计
过程要复杂得多。比如，实际设计中色差是不能独立于像差单独校
正的。无论何时色差不能达到要求，整个设计过程只能重新开始。
镜头的图像质量要求越高，重新设计的次数越多。一只高级镜头重
新设计几百次宣不稀奇。

after · 发表于 2003-9-24 22:52:00

顶。
Meniscus lens - An early lens for landscape photography was a single
positive meniscus lens (in fact, used in a camera obscura before
the invention of photography). Maximum aperture about f/15.
Rapid Rectilinear lens - two cemented doublets, symmetrical, about
f/6 to f/8 (fast for its day, hence Rapid). Historically very
important, given the slow emulsions of the day.
Protar - two cemented doublets, not symmetrical, fairly slow, can
cover a wide field (70 deg or more?). Reputedly not as sharp as
modern lenses, but for large film sizes it covers a lot in a small
package. There are some convertible Protars (giving multiple focal
lengths through exchanging lens cells or using single cells - single
cells will have chromatic aberration). Examples: Zeiss, BL Protars;
others?
Dagor - two cemented triplets, symmetrical, f/6.8 or 7.7 usually.
Wide field, supposed to cover 70 deg at f/16 or so, 75-80 deg when
stopped down further. Spherical aberration when wide open, watch for
focus shifts. Late model Dagors are something of a fetish-object and
can go for absurdly high prices, but earlier ones can be found at more
reasonable levels. Do a Dejanews search (www.dejanews.com) in this
newsgroup for tons of posts about Dagors. Examples: Goerz Dagors;
other firms’’ Double Anastigmats.
Angulon - two cemented triplets, symmetrical, like a Dagor but with a
different shape for one of the cemented interfaces, f/6.8. Wide field,
something like 80 deg. Spherical aberration/focus shift again.
Angulon is a trade-name, I don’’t know if anyone besides Schneider
made lenses of this design. Newer wide angles are sharper and have
more coverage but tend to be huge; older wide angles such as Angulons
and Dagors might be friendlier for field use, especially in large
formats (a 165mm Super Angulon is about the size of a 10 pound barbell).
Double Gauss - many variations. In its simplest form it’’s two
air-spaced doublets of two meniscus lenses, and is symmetrical. The
design is varied by different choices for the shapes of the elements,
replacing some of the elements with cemented or airspaced doublets,
large deviations from symmetry, and so on ... The Kodak Wide Field
Ektars are 4-element double Gauss designs, f/6.3, covering about 80 deg
stopped down. Some older wide angle lenses are also 4-element double
Gauss, as are the Topogon and Metrogon wide-angle aerial lenses.
Also, most fast normal lenses for 35mm and roll-film cameras are
extensive modifications of the double-Gauss design, descending from
the Planar design. Examples: Kodak W.F. Ektars; others (Wollensak
W.A. Raptar?)
Cooke triplet - two airspaced elements in front of aperture, one
behind. Early medium-aperture (f/4.5 - f8 or so?) design.
Tessar - derived from Cooke triplet, two airspaced elements in
front of aperture, cemented doublet behind. Can be made fast,
even up to f/2.8. Moderate coverage, generally 55-65 deg.
Classic simple medium-fast normal lens. Most lenses found
on press cameras are Tessar types. Examples: Zeiss Tessar;
Kodak 127/4.7 and 152/4.5 Ektars (note Kodak used Ektar for
all its premium lenses, it doesn’’t specify a lens design);
some Wollensak Raptars and Graflex Optars (again, Raptar
doesn’’t specify a particular lens design); Kodak Commercial
Ektars (f/6.3, 64 deg coverage); Schneider Xenar.
Heliar - also derived from triplet, has three elements in front
of aperture, cemented doubled behind. Also a fast normal
lens, with 55-60 deg coverage.
Dialyte - two airspaced doublets (one elements convex, one concave),
symmetrical. This type of lens is often used for process lenses,
which can be found relatively inexpensively in barrel mounts.
Although process lenses are designed for close-up use, the dialyte
design maintains its corrections fairly well as the magnification is
changed (so Kinglake says) and these can be used at infinity.
Dialytes are relatively slow, commonly f/9-f/11, and have somewhat
limited coverage, 45-50 deg. Examples: Goerz Celor, Dogmar, Artar;
Kodak 203/7.7 Ektar; Rodenstock Apo-Ronar; Wollensak Apo-Raptar; no
doubt many others.
Plasmat - the basic plasmat design is symmetrical, each half being a
cemented doublet with a meniscus element behind it. There are
variations with more elements etc. The plasmat combines medium speed
and wide coverage, usually f/5.6 to f/9 and coverage 64 - 72 deg.
It’’s now the dominant design for modern LF lenses of normal length.
Actually, it’’s an old design, but did not become widely used until
lens coating became common. Plasmats are technically cconvertible by
using the rear element alone, but they won’’t be as sharp that way and
will have chromatic aberration. Examples: Schneider Symmar and
G-Claron, Rodenstock Sironar, Nikkor W. There are also newer variants
from e.g. Rodenstock and Schneider with even more coverage (which
are really huge and expensive).
I haven’’t really addressed telephotos or modern wide-angles. True
telephotos have a negative element in the rear which makes the focal
length longer than the bellows draw, and usually have an obvious name
like Tele-Something. Modern wide-angles such as Grandagons, Super
Angulons, etc. seem to be derived from the Biogon design - generally
not quite symmetrical, with very large meniscus front and rear
elements, and loads of coverage.
Remember the diameter d of the circle of coverage of a lens,
the focal length f, and the coverage angle theta, are related by
d = 2 * f * tan(theta/2).

cyclone · 发表于 2003-9-27 01:17:00

没有图啊，能不能扫描进去啊。

华山老妖 · 发表于 2003-9-27 16:46:00

好吧，我扫描了传上去，不过干什么事都需要光电币，要知道，我是穷人呀！那么就......，收一点吧，意思意思！

cyclone · 发表于 2003-9-27 17:30:00

应该的，应该的，呵呵

华山老妖 · 发表于 2003-9-29 18:43:00

图1

华山老妖 · 发表于 2003-9-29 18:44:00

图23

cyclone · 发表于 2003-9-29 19:25:00

thx!

华山老妖 · 发表于 2003-10-10 01:52:00

想了一想，都是兄弟，要钱不就见外了不是，赠送给各位了！

mykosovo · 发表于 2003-10-10 02:02:00

好样的！顶！

smguang · 发表于 2003-10-18 18:49:00

好！

wang-li-peng · 发表于 2012-3-1 09:49:29


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[推荐]『徕卡设计师谈镜头设计』