Imaging the surface of a half ball lens

[lferreir]

Hi,

I'm new to this forum and I have an application where I want to image an object that is in contact with the round side of a half ball lens. I've attached a brief project description.

I think this topic on optics is suitable for the Differential Geometry forum, but please let me know if it's not.

The object in contact with the lens is shoulder joint cartilage and I do have the ability to illuminate it by inserting a light source behind the cartilage surface. The illumination wouldn't be great but probably enough to determine contact area with the lens, which is all I want.

I'm not an expert in this field but I think that with the object being in contact with the lens (i.e. zero working distance), that there is no refraction.

I need to know the focal length for a half ball lens of about 20 mm radius and the size of the sensor for a circular contact area on the lens with a 10 mm diameter.

The challenge I'm having is determining the correct equations to use without a working distance.

thank you

 

[jvicens]

Hi there,

Welcome to the forum! Your project sounds really interesting. I agree that this topic would be suitable for the Differential Geometry forum as it involves understanding the curvature of the half ball lens and its impact on imaging an object in contact with it.

You are correct that with zero working distance, there is no refraction. This means that the focal length of the half ball lens will not be affected by the distance between the lens and the object. The focal length of a half ball lens can be calculated using the following equation: f = r/2, where r is the radius of the lens. In your case, the focal length would be 10 mm.

To determine the size of the sensor needed for a 10 mm diameter circular contact area on the lens, you can use the equation for the magnification of a lens: M = s'/s, where M is the magnification, s' is the size of the image, and s is the size of the object. In this case, s' would be 10 mm (the diameter of the contact area on the lens) and s would be the size of the object you are imaging. You can then rearrange the equation to solve for s, which will give you the size of the sensor needed.

I hope this helps. Let me know if you have any other questions or need clarification on anything. Good luck with your project!