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# Diffraction Limted Optics

Jul 19 2006 09:12 AM |
Cary
in Optical Theory

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**Diffraction Limited Optics**

I continually see statements of “diffraction 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.

In order to first understand what the statement “diffraction limited” means, we need to understand what diffraction is and how it effects image formation in a telescope.

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–particle duality.*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.

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.

Next we examine the resulting spot diagram for the exact optical center of the mirror.

You’ll note that you will find a small spot centered in a larger circle. Along side is a scale bar of 10 microns (10/1000

^{ths}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 “blows” 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 “diffraction 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?

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.

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 º wave and applied a Monte Carlo algorithm. The resulting geometric focus blur still just falls within the diffraction disc and again the performance is “diffraction limited”.

Next we adjust the tolerance level to ? wave on the wave front and we now see that the geometric focus starts “spilling” 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 “diffraction limited”.

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.

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.

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.

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.

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.

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.

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 “breaking down” on objects larger than this size.

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’ve changed the focal ratio of our sample parabolic mirror to f/8, doubling the focal ratio.

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 º degree!

In conclusion:

- We can see that the approximate wave front tolerance for a parabolic mirror to deliver diffraction limited performance at the CENTER of the field of view is º wave p-v deviation.
- When we talk about diffraction limited performance we must qualify over what field of view.
- Longer focal lengths give larger diffraction limited fields of view!

- shahram likes this

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