# view angle independant focal point

Is there any way to design a lens or system of lenses where I see the same part of the image below the lens, irrespective of direction from where I am viewing. In the image uploaded, there is a black dot near the focal length of the lens. This black dot will be visible magnified to me if I look at it from above. but if I look at it from sideways, the focal point will shift. So, is there any lens or lens system that can be designed where I can see the same magnified black dot, whether I am viewing the dot in direction perpendicular to it or at 90 degrees in either direction? A lens or lens system where focal point is not dependent on the direction of view? The light rays can be assumed to be collimated as viewing will be from a distance.

• A lens is (to first order) an optical Fourier transformer that goes from angle relative to the optical axis to displacement on the focal plane, so the answer is negative. What you are trying to do also violates the second law of thermodynamics since your design, as shown, could actually change the Etendue: en.wikipedia.org/wiki/Etendue. – CuriousOne Mar 23 '16 at 7:27
• Thanks for the reply....I don't know much about Etendue, but if what you say is correct, how does fish eye or wide eye lens focus light from 180 degrees to a single point..? does this not mean that if I view an object kept at say focal length or near focal length, then I should be able to see the magnified version of that object from any angle that I View. we did – devalvyas Mar 23 '16 at 9:56
• now magnification is given by M=F/(F-d), F being focal length and d being distance of the object- X in our case. Say we adjust the magnification to 10, so we will be able to see 10 times bigger X from the lens. Now since fish-eye lens brings all light to the focal length from entire 180 degrees , will it not mean that I will see magnified X from all the 180 degrees and will not see W and Y at all? – devalvyas Mar 23 '16 at 10:24
• All I am interested is in having an arrangement where I can only see magnified X from all directions and not see W and Y...that is, I want to see say only 33% or say even 50% of the focal plane only from all directions, I want the remaining 66 or 50 % to stay hidden...irrespective of the angle from where I am viewing. – devalvyas Mar 23 '16 at 10:25
• Going by the example, I have arc length L of say 10mm so I will define my focal plane a circle having area of pi*D^2/4= 314/4=7.85 sq mm approx. Now I want my lens to focus only on say "the same" 2 to 3 sq mm area in the middle only and make the other peripheral area hidden when viewed from lens from any direction....may be I have framed by question wrong, but I am trying to achieve the above and want to know if its possible... – devalvyas Mar 23 '16 at 10:32

You're on the trail of a "fisheye" lens. If you spend enough money, you can get a lens with greater than $\pi$ Field of View in elevation. (Yes, for real) Here's one way to look at it: if you can see the same image on the focal plane wherever you are, then the focal plane can "see" you wherever you are.

Let's take a look. It is very useful that you've provided the images. Basically what you say that every point on the surface of this "lens" will "emit" in every direction. Well I guess one just need to glue a paper on this lens so that it will nicely scatter the light, i.e. emit in every direction.

Will the image look like a point or a circle from the distance? More like a circle of course. But this is a consequence of the finite size of the aperture of your eye and restrictions which you put on the "lens".

This is probably not the kind of device you wanted. But the one which fits your images

• Not really useful. – Carl Witthoft Mar 22 '16 at 15:16