Why doesn't central obscuration put a big dot in the middle of a PSF for a centrally obscured optic?

I'm confused as to how central obscuration effects the PSF. Low pass filters make sense since they are inherently oriented with dealing with spatial frequency, resulting in blur in the spatial domain. But central obscuration confuses me in the fact that it is inherently a spatial property, obscuring what you see, but intuitively not certain frequencies outside of the obscurants shadow.

In order to help me understand this concept I looked at this pdf : http://www.beckoptronic.com/media/22126/Beck_TN_Central_Obscurations.pdf which helped me see what the PSF would look like in such systems. However now I'm very confused as to why I'm only seen a tiny dot in the PSF given a 20% central obscuration. In the real world, when I put my finger in front of my eye, I can see clearly that it is blocking my view.

If my finger instead was a mirror that only showed the light It was not blocking I would still similarly assume that I was missing part of the image, as I assume it would appear warped, or it would show the central part of the image being blocked illustrated here

Yet this is the real PSF of a 20% centrally obscured optic:

Why aren't we seeing PSFs with a lot bigger black dots in the middle of them for these cameras when these obscurants are blocking 20% of the apeture?

The difference between what you expect and what that PDF shows seems to come down to an error in your second diagram. In particular, if you compare your diagram to the diagram shown in that PDF, you see that the incoming light rays are parallel in the PDF, but are sharply diverging in your diagram. Reflecting telescopes and microscopes are designed to focus on something small quite far away, rather than whatever it is your diagram would be looking at. So imagine a point just above the axis of your telescope, but way off to the right side. It sends a light ray horizontally into the telescope, and just above the secondary mirror, so that it goes on to hit the primary mirror. That primary is shaped by design to reflect such a light ray back to the secondary, and then into the eyepiece. For a microscope, it might be designed so that the light ray could even come in at an upward angle but still make it to the eyepiece. So the only place directly in front of the tube where light couldn't reach the eyepiece would be where it can't even reach the primary mirror — which is actually pretty close and directly in front of the secondary.

• With out reference, I'm deeply confused by your example of things like "way off to the right but horizontal". Saying that makes me think of a impossible optical system. Same with "light could come at an upward angle". For example, I'm interpreting what you are saying as a light ray hitting horizontally on the tube of a telescope... where no light can enter... thus the whole thought experiment doesn't make sense to me. Nov 1 '18 at 20:16
• No, it shouldn't hit the tube. The right-hand side of the diagram is open to light rays coming in, isn't it? If you ignore the secondary mirror for a moment, just imagine some point off to the right of your screen that's basically in line with where the tube is pointing. It should be able to emit light rays that enter the front of the telescope, correct?
– Mike
Nov 1 '18 at 20:22
• It appears I'm interpreting horizontally differently than you are. I think the term horizontal was ambiguous to me,eg. in reference to what? Where? Similar story with "way off to the right". I believe now what you were talking about is a straight line into the right most portion of the aperture, but what I interpreted is was a point orthogonal to the lateral axis of the telescope, coming horizontally into the tube of the telescope. Okay, so yes, I agree that things to the far right of the aperture should be able to emit light into the telescope, what next? Nov 1 '18 at 20:28
• Just to be clear: by "horizontal" I mean with respect to your diagram, as in the literal $(x,y)$ values of pixels in that diagram, and confining everything to be in the plane of your diagram. So, I guess another way of saying what I'm saying is that the "UNSEEN" region in your diagram has the wrong shape. For example, take a point inside that region, but near the top right part of it. That can emit a light ray that will hit the primary, and the primary is actually designed to get that light ray into the eyepiece.
– Mike
Nov 1 '18 at 20:35
• That confuses me, take the first image, if I take a ray, and I move way far away, but move up from where the obscurant is,I physically still won't be able to see the ray of light, because the obscurant blocks an conal range of light, not a cylinder. No matter how far out I am looking, I'm still going to lose 20% of my area of aperture to the obscurant. If the unseen area is not supposed to be a cone, what is it supposed to be and how do you rectify that with respect to the first image? Nov 1 '18 at 20:42

Thanks to Mike I realized had my ideas of the optics wrong, mirrors aren't eyes, or even convex lenses, so they aren't going to have the same perspective, parts of the mirror will actually be able to see directly behind the obscurant, like in this diagram:

we have light emitting from a point directly behind the obscurant, and yet we are still going to receive light from it, because from the perspective of the mirror, it can still receive light rays from it.

What I should have done is think about where the light rays are coming from, rather than try to relate it to how my eyes see things.