Lens questions from a software engineer

[tappo]

Hello everyone,

I am a software engineer and know very little about lenses but am trying to learn. I am confused about the differences between convex-convex and plano-convex and how to decide how to design an actual plastic lens for a real world application.

Here is an example (not real world, but bar codes seem easy to understand since 1D):
Lets say I want to make something like a bar code scanner for simple bar codes. The bar code is 40mm wide. And I have a 1D camera sensor, which is only 10mm wide. And then let's say the sensor is 10mm away from the bar code. So somehow I need to scale the bigger barcode to the smaller area of the sensor.

Here are some questions:
1) Since everything is 1D, it seems like a cylindrical lens should/could be used, is that true?
2) What kind of lens should be used? (plano-convex or convex-convex, or something else?), this part is very unclear to me.
3) How can I compute the curvature of the lens to get the desired distance between sensor and bar code?


Many thanks for any hints and ideas,
Tappo

 

[Andy Resnick]

Bar code scanners don't use imaging- they use what's called an f-theta lens to convert the angular motion of the scanning laser to linear motion at the (linear) detector.

But- you want to image the bar code. All you want to do is *demagnify* the object. You must first specify some properties about the system: distance from the bar code to the lens, distance from the lens to the detector, size of the bar code, size of the detector.

Then, for the most simple type of model (a single lens), you can use the thin-lens formula to calculate the focal length (and curvature) of the lens. Whether to use a planoconvex or biconvex is dependent on the aberrations present, but at this introductory level I would recommend not worrying about it.

You could use a cylindrical lens, but those are more expensive than plano-convex lenses. Plus, the alignment is more difficult.

In the real world, this is a solved problem- what are you doing differently?

 

[tappo]

Hi,
thanks for the answer.

I am not trying to do anything new,but I try to understand how lenses work using some examples I can think off.

Cylindrical lenses:
I might be using the wrong word. I thought a cylindrical lens can ALSO be plano-convex or anything else, and cylindrical just means that the lens is only curved along one axis rather than along two axis, which I thought would make it cheaper.
The main reason why I thought about cylindrical lenses is because it seemed to me that since the camera is 1D only, a cylindrical lens would take up much less space, since it can be a thin slice of the cylinder, while a round lens would take up more space.
Pleae tell me if I am misunderstanding things or use the wrong terms.

I made a sketch on how the setup I amthingking about would look like, please excuse my bad artwork.

http://randomimages.host-ed.net/index.html

Many thanks again,
Tappo

 

[reasonableman]

Lenses are not that complicated or at least they are not complicated until you get to a level that only computer modelling is useful. So what you've said is correct.

A plano-convex lens simply has a flat side and a curved side. A cylindrical lens can be plano-convex.

As to cost for lenses, like many things, it is not easy to derive cost from complexity. Some lenses are cheaper just because they are more common.

I recommend looking at some optics catalogues (Thor Labs, Edmund Optics). They often have small technical notes and you can see prices etc.

 

[Andy Resnick]

I made a sketch on how the setup I amthingking about would look like, please excuse my bad artwork.

http://randomimages.host-ed.net/index.html

Many thanks again,
Tappo

Your drawing is fine, but cylindrical lenses are rarely used in practice. Your system (as drawn) requires very tight tolerances on the alignment of the barcode to the lens and detector. Slight rotations of any of those elements will kill the system.

But for what you are thinking about, you are on the right track.