Direction or angle independent image formation in lens

[deval vyas]

Is there any way to design a lens or system of lenses where I see the same part of the image, irrespective of direction or angle of view. The light rays can be assumed to be collimated as viewing will be from a distance.

Actually- I am looking at focusing on a point or specific area of the object plane below the lens. In the attached diagram, say there are three letters w, x and y written on focal plane of the lens of arc length L and focal length F and three observers are looking at it from 3 directions, then all of them should be able to see magnified version of X. W AND Z SHOULD REMAIN HIDDEN EVEN WHEN OBSERVED FROM ANY DIRECTION.

Another way, I am interested in seeing say only 33% or say even 50% of the object plane only from all directions, I want the remaining 66 or 50 % to stay hidden...irrespective of the angle from where I am viewing. Going by the example, I have arc length L of say 10mm so I will define my focal plane a circle having area of π*D2/4= 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...

We can say I am looking at system which is opposite of Lenticular Lens. In lenticular lens I see different images from different angles. Here I want same "magnified" image from all the 180 degree angle of view.

 

[jwinter]

I couldn't see any attached diagram, but the camera app on a mobile phone should pretty much give you what you want? Looking at the screen and moving your head around almost the full 180 degree angle of view leaves the same image visible on the display - and that image can be zoomed into represent quite a small fraction of the "object plane" (depending what you mean by that).