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area of the lens without distortion

A spherical lens has an aplanatic point (no spherical aberration) only at a radius equal to the radius of curvature divided by the index of refraction of the lens material. Crown glass typically has an index of refraction of 1.5, so if the radius of curvature of a particular lens is 1.0, then the aplanatic radius is 1.0 / 1.5 = 0.66666..., which is about 67% of the diameter of the lens. That gives an area of only 43% in the middle of the lens that will have no spherical aberration. Images outside this area will show spherical aberration.

Coddington magnifier

I am trying to find information about the calculation of the shape of the groove in a Coddington magnifier. I suspect that it is related to the aplanatic point. I believe the groove may be cut to the aplanatic point in order to block light from outside the useful range of the lens. Unfortunately, I have found little information on how this groove is actually calculated.

Diopter vs. Magnification Power vs. Magnification Factor

These units are often confused in low end products. It is not uncommon to see cheap magnifiers and loupes described as "40X magnification". Really, the sales person probably did not understand the difference. A simple lens or even a loupe with 40X magnifying power is very unlikely. In this case the lens is more likely a 40 diopter lens, which would have an 11X magnification power.

What is even more confusing to people is that Magnification Power, usually written as 4X, 10X, 20X, etc. is not the same as Magnification Factor. The X is confused with multiplication, so often people think it's a simple multiplication factor. Just add 1 to Magnification Power to get the Magnification Factor. So, a 1X magnifier gives a factor of 2 magnification -- an image will be twice the size. The difference is simple.

Magnification Power = diopter / 4
diopter = 4 * Magnification Power
Magnification Factor = MP + 1

Why have both diopter and magnification power when they are both so similar and easy to convert? It's a matter of convenience to have slightly different terms and numbers with different aspects of optics. The diopter term is used when talking about focal length and how far away two beams will converge after passing through the optical system. With Magnification Power and Magnification Factor you are usually asking about how much bigger or small will an image appear. The numbers are not actually different, they are just used differently as a convenience.

Real Image vs. Virtual Image

The sense of these two terms may seem reversed to many people. The image you see in a mirror is a virtual image. The image projected onto a screen by a video projector is a real image. This may feel wrong because the image in a mirror looks realistic and natural; you can move around and see objects from different perspectives; you can change the focus of your eye to make distant objects sharp and near objects blurry, and visa versa. Whereas an image from a projector is flat and lacks perspective (your brain my imagine depth and perspective based cues); you cannot walk around the room to see objects in the image change perspective.

(even 3D projections systems do not produce an image that behaves the way a natural scene does. You cannot walk from the left side of the screen to the right to see objects in the image from a different perspective). Your eyes cannot change the focus of the image by looking from near to far. You need to think a little differently. The image you see in a mirror is obviously no of real stuff. The light you see has not actually colored the glass. The projected image is real in the sense that photons of various colors have actually converged on the screen. Those photons color the location of the object they scatter from. They literally change the color of the screen (not permanently, of course). If you look at a point in a real image that is red then that point will appear red even if you change your perspective. The point looks red to everyone in the room. That point on the screen really is red. This is not true of a mirror. A point on a mirror that looks red to you may look completely different to someone standing at beside you. The image you see is yours and is not the same image someone else in the room sees, yet you are nothing looking at the same mirror. The image you see is virtually there, it is not actually there.

Remember, a real image does not imply realistic.


LASER safety

Some LASER diodes use an optical pump to drive a LASER medium. For example, green LASER diodes use IR from a separate LED. These pumping frequencies are usually filtered from the LASER output, but unintentional leakage can occur. Your LASER safety goggles should be designed to block all frequencies that may be emitted. Remember, you can't see IR light, so you wouldn't easily be able to tell if it were leaking.

The item #AGFKTP59X (also called model #LSG-KTP-NF-6) from http://www.laserglow.com/AGF will block 190-534 nm, 720-740 nm, and 740-1064 nm.