器材知识：光学衍射极限
Diffraction Limited OpticsI continually see statements of 揹iffraction limited optics?in the industry and this generates an astounding amount of discussion to exactly what this is and what it means. Therefore, I write this paper to try to explain what this is and what it means to you ?the telescope user.
我不断的看到有关光学衍射极限的评述。光学衍射极限是什么？有什么意义？我写这篇文章就是尝试对望远镜爱好者解释是光学衍射极限是什么以及有何意义的问题。
In order to first understand what the statement 揹iffraction limited?means, we need to understand what diffraction is and how it effects image formation in a telescope.
要理解衍射极限的意思，首先我们要搞明白衍射的定义以及衍射如何影响望远镜的成像。
From Wikipedia, the free encyclopedia
Diffraction is the bending, spreading and interference of waves when they pass by an obstruction or through a gap. It occurs with any type of wave, including sound waves, water waves, electromagnetic waves such as light and radio waves, and matter displaying wave-like properties according to the wave杙article duality.
衍射就是指当波通过一个小孔，或者一个障碍物体，发生的波的弯曲、扩散和干涉的现象。衍射发生在任何形式的波上，包括声波，水波，电波以及光波，表现出来的波浪形的特性都遵从波粒二象性。
From this definition we can see that as light waves pass by an obstruction or EDGE of an optic, they are bent. This process is diffraction. Since our telescope mirror has an edge (round) the impinging starlight gets diffracted at this edge of our telescope mirror (refractors do this to!). Therefore, instead of incoming light being focused to a perfect geometric point, the diffraction effect spreads the light into a disc with rings surrounding it. This disk is known as the Airy disc.
从概念中可以看出，光波通过障碍物体时或视觉边缘，会发生弯曲，这个过程就是衍射。同理，我们镜子的反射镜也有一个边，在这里也会造成衍射（折射也同样）。因此，由于衍射存在，我们很难把入射光线集中在一点上，衍射使最终形成一个圆盘或者在外圈形成一个圆环。这个圆盘就叫做爱里克斑。
If we examine 12 inch f/4 parabolic optics with ray tracing software we can explore this diffraction effect. Below is a ray trace of the system layout.
如果我们用12英寸F4的抛物线镜子，使用光线跟踪软件，就可以揭示衍射的效果。下面就是光线跟踪的示意图：
http://www.cloudynights.com/images/diffraction/image002.gif
Next we examine the resulting spot diagram for the exact optical center of the mirror.下面我们检查镜子中心的结果：
http://www.cloudynights.com/images/diffraction/image003.gif
You抣l note that you will find a small spot centered in a larger circle. Along side is a scale bar of 10 microns (10/1000ths of a millimeter). The small spot represents the size of a star image as if it were perfectly geometrically focused without the effects of diffraction. The outer circle represents the Airy disk of the REAL star image. So even though the geometric focus is smaller than the diffraction disc, the star image 揵lows?up to the size of the outer circle. In this case, one could say that the performance of this optic is limited by the diffraction effects, hence the term 揹iffraction limited? However, AS USUAL, there is more to the story. The first question that arises is what does it take in terms of surface error, to obtain diffraction limited performance. The second part of the story is over how much field of view is the performance considered diffraction limited?
你会注意到，在大的圆环中有一个很小的点。旁边的刻度是10微米。这个小点代表星像，好像光都聚集到了一个点上，没有收到衍射的影响，但是外圈的大圆其实就是爱里克斑。因此，尽管光点比爱里克斑小很多，但是真正的星像仍然应该是外圈的大环。因此我们可以说，这样的结果就是受了衍射的影响，也就是衍射极限。这个实验还说明其他的问题。问题就提出来了：根据镜子表面的误差，衍射如何起作用？对视场的影响上，起多大的作用？
Before we get too deeply into thiese subjects, I have to stress that we are talking about only the extreme center of our parabolic mirror and once we start examining the field of view (which we will) things change.
在我们深入研究这个问题前，我们要强调我们讨论的仅限于抛物面镜子的正中央部分，来看有关的变化。
So how much surface deviation can we tolerate before our optic is no longer diffraction limited? Below you will find a repeat of our spot diagram showing the geometric focus as well as the diffraction disc (the circle). This time the geometric focus is a bit of a blur. This is due to the application of tolerance calculations in the ray trace software. I allowed the resulting wavefront to vary by ?wave and applied a Monte Carlo algorithm. The resulting geometric focus blur still just falls within the diffraction disc and again the performance is 揹iffraction limited?
那么多大的镜面误差是是我们能够容忍的呢？下图你可以看到一个焦点处的点状图。这一次焦点显得有些模糊，这是由于光线跟踪软件的误差造成的，这个误差是允许的。这个模糊的焦点仍然落在了大的衍射环内，这也是衍射极限限制的结果。
http://www.cloudynights.com/images/diffraction/image004.gif
Next we adjust the tolerance level to ? wave on the wave front and we now see that the geometric focus starts 搒pilling?out of the diffraction disc. It becomes obvious that the performance is no longer limited by the diffraction of the system. This optic is not 揹iffraction limited?
当我们继续放大可以容忍的误差，下面这张我们可以看到，焦点处的斑点已经散落在衍射圈的外面。很明显，整体的表现已经不受衍射极限的限制。
http://www.cloudynights.com/images/diffraction/image005.gif
Now we should have a good understanding of what the term diffraction limited means, however as I mentioned earlier there is a bit more to the story. When we use the term diffraction limited, we must also qualify where in the telescope field of view this is happening. Is it happening at the exact center of the field of view only? Does this extend to the edge of our eyepiece or camera field of view? How big is this area? If we are to truly understand the performance of our telescope we must answer these questions.
现在我们可以很好的理解衍射极限的意思了。当我们使用衍射极限这个概念时，我们必须限定是在望远镜的哪一个部分。这个现象只会发生在镜子的中心部分么？会延伸到目镜的边缘或者是像机的视场内么？这个区域有多大？如果我们要真正了解我们望远镜的表现，我们必须回答这个问题。
First, when we talk about the image performance, we have to qualify how big the field of view is. We talk about this in terms of angular field.
首先，当我们讨论像质表现时，我们必须限定视角的大小。我们依照角度来讨论。
To help understand this, we can imagine viewing a single star in the exact center of the telescope eyepiece (field of view). This star is at the zero field angle and, as in our example above, we are enjoying a diffraction limited view of this star. But what if we view more than one star at a time? What if we view a cluster, a galaxy or the moon? These objects extend outward from the center of the view towards the edge of the filed of view provided by our eyepiece or camera.
为了有助于理解这个问题，我们可以想象，在目镜的正中央，看一颗星。这颗星的角度就是0度，我们当然很乐意进行这样的单星测试。但是，如果同时有多颗星存在怎么办？如果我们看的是星簇，星系或者月亮怎么办？这些物体都会从目镜的中心延伸到边缘。
Next we present a spot diagram with our original star in the center of the field of view (left), but this time we add a star at the edge of a ? degree diameter field of view (at right). Here we see that the central portion of the view is diffraction limited, but the edge of the field is far from diffraction limited. The coma blows the star image up way beyond the Airy disc, which is the black circle.
下面我们再提供一个点图，左面是我们一开始提供的星点，只在视场的中心位置；右面是我们在视场的边缘增加了一颗星。我们看到，中心部分是衍射极限的作用，但是边缘已经远远超出了衍射极限，慧差使得星点的图像超出了爱里克斑的限制。
http://www.cloudynights.com/images/diffraction/image006.gif
The obvious question becomes: is this diffraction limited or not? The answer is both. This optic is diffraction limited at the center field but not at the edge. This in turn leads up to asking the question of exactly how large is the diffraction limited field of view.
现在问题变成：这个是不是衍射极限的作用？答案是共同的作用。衍射极限只在中心部分起了作用而不是边缘。反过来，又引出一个新的问题，衍射极限的视角到底有多大？
In turn we present another spot diagram with several points in the field of view to demonstrate the portion of the view that is diffraction limited as well as what is not.
我们再提供另一个点图，这个图是在视场内提供了几个光点，来说明刚才所说的共同作用的道理。
http://www.cloudynights.com/images/diffraction/image007.gif
What we see from this spot diagram is that a small central portion of the field of view is diffraction limited (extreme upper left) and then at some point, the diffraction limit is exceeded (lower left field position). From the above example we see that up to about 5 times the diameter of Jupiter is diffraction limited and then the performance starts 揵reaking down?on objects larger than this size.
我们看到，左上图，衍射极限只是集中在中心很小的部分，在用多点的测试中（左下），衍射极限超过了爱里克斑。从上面的例子我们可以看出，其他作用的影响远远大于衍射极限的影响。
Finally, we will see that the diffraction limited area in the field of view is proportional to the focal length. The longer the focal length, the larger the diffraction limited field of view is. Again we present a spot diagram with the same fields as above except that we抳e changed the focal ratio of our sample parabolic mirror to f/8, doubling the focal ratio.
最后我们将看到，衍射极限影响的区域与焦距是成比例的。焦距越长，衍射极限作用的区域越大。我们还是用上图，只是改变焦比，把焦比改成F/8：
http://www.cloudynights.com/images/diffraction/image008.gif
From this spot diagram, we can see that the diffraction limited field of view has grown by almost a factor of 5 times and the diffraction limited field of view is almost ?degree!
从这个点图，我们可以看出，衍射极限作用的区域随之增长了5倍（我理解的是，更多的斑点被限制在爱里克斑内，也即发散出去的斑点面积反而小了）。
欲了解更多内容，请看
http://blog.sina.com.cn/u/4c6ee55101000a7t
[ 本帖最后由 我爱祖祖 于 2007-6-21 16:56 编辑 ] 好贴～～～加精啊～～～::42:: ::42:: 图片并茂,很详细啊。 现在这方面的文章，也是叫好不叫座，没办法。
我也是玩了这么长时间镜子以后，突然发现作为一个爱好者这些知识真的很有必要，可能大家都不感兴趣把::0020:: 原帖由 我爱祖祖 于 2007-6-21 19:15 发表 http://www.astronomy.com.cn/bbs/images/common/back.gif
现在这方面的文章，也是叫好不叫座，没办法。
我也是玩了这么长时间镜子以后，突然发现作为一个爱好者这些知识真的很有必要，可能大家都不感兴趣把::0020:: ...
你倒是发啊::0020:: 呵呵，不好意思，刚刚发。
你的头像有点太粗旷了把::39:: ::37:: 好贴！学习中！ 原帖由 我爱祖祖 于 2007-6-21 21:00 发表 http://www.astronomy.com.cn/bbs/images/common/back.gif
呵呵，不好意思，刚刚发。
你的头像有点太粗旷了把::39::
他是我偶像::17:: ::17:: 还以为是你的照片呢::37::
一个充满忧郁眼神的男人 不错，学习！::39::
页:
[1]