# How to convey the image of a 14 mm object through a thiner (8 mm) pipe?

My setup and constraints are the following (see figure below):

• A rectangular pipe (~50 mm long, section 8 mm).
• The pipe has an apperture at one of its end, which is larger than 14 mm.
• A 2D object (a sign) that can be represented as a segment of length 14 mm.
• The pipe can embed any number of optical element, as long as all of it fits into the 8 mm.
• At the other end of the pipe, there can be several complementary optical elements to restore the image, without any size constraints.
• A camera sensor (the size of the sensor does not matters here).

What I want to do is be able to convey the image of the object through the pipe, and obtain at the other end of the pipe an image that is not distorted (e.g. a change of apparent size is ok, but a tilted image is not.) and that can be retrieved on a camera sensor.

A simple mirror with a 45° angle (to reflect without distorsion), would be too close to the object to be able obtain the entire image of the object.

So far I have tried to use a tilted mirror, with a small angle which reflect rays coming from the object parallel to the pipe into a lens and then into the sensor, but then the image is tilted and cannot be focused entirely (the image plane is not perpendicular to the guide). I have also tried to add a second mirror parallel to the first to correct the image plane, to no avail. I was also thinking of a system of lenses at the entrance of the guide, to "compress" the image before reflecting the image into the pipe with a 45° angle so that there is no distorsion, but my intuition is that the optical system will be too big to fit the 8 mm constraint.

Has anybody an idea as to whether this is possible at all ?

• Can you edit your question to explain what "a guide" is in this context? And "a segment"? Can you add a caption to the image explaining what it represents? – Transistor Nov 20 '20 at 20:03
• The guide is a rectangular pipe, 8 mm wide (interior) and the segment is the object to take a photo of. In reality, the segment represent a 2D object to be photographed. Editing the description to try to clarify and to complete the diagram – yco Nov 21 '20 at 21:46
• So it's like an 8 mm bore-scope with a right-angle lens trying to measure a 14 mm object but at what distance from the opening in the guide? Why isn't the sensor up where the mirror is? – Transistor Nov 21 '20 at 23:21
• Yes except the guide of the "bore-scope" is rctangular and not flexible. 1) The object is supposed to be directly on the 14 mm opening on the side of the bore-scope. 2) Having the sensor directly in front of the object would mean using a fish-eye lens, which would introduce a huge distorsion in the resulting image, if it can be focused at all. – yco Nov 23 '20 at 8:21