best form vs bi-convex vs plano convex vs achromat

[kecked]

Doing a little learning about lens and came across the best form lens. It seems to me the best form lens is a lot like an achromat at least in shape. Any comments on these shapes for the community? For most of our uses these lens seem pretty much interchangeable using a coherent beam with bi being the best choice balancing cost and performance. Pretty complicated stuff when you really try to learn the math.

http://www.astro.caltech.edu/~lah/ay...tal-Optics.pdf

[catalanjo]

Hey man, thanks for the link.
I suppose now we wait for Eric to comment!
Cheers

[kecked]

point is for us to educate ourselves so we don't have to keep bugging him. He's amazing but don't you think its time for us to educate ourselves! I sure as !@#$ ain't going to get the math but I will at least understand the basics.

[catalanjo]

That's true as far as theory is concerned, ... but to confirm theory in practice requires considerable resources, and as well as having resources, he is eminently practical in his approach, which is what makes his contributions so valuable ....at least to me !
Cheers

[krazer]

It of course depends on your application, but for an application where you are taking a collimated beam and focusing it to a spot (as would be used for a telescope or diode collimator), a bestform will outperform a plano-convex which will outperform a bi-convex. You can do better with a doublet (such as an achromatic lens), and for monochromatic light you can always do the best with an aspheric lens.

The difference between a bestform or achromat or ashpere has to do with the level of optimization applied to the lens design. When designing a plano-convex lens your only degree of freedom (for a given focal length and optical material) is the lens thickness, and for almost all applications it works out that the thinnest possible lens will perform best. When designing a bestform lens the lens maker has 3 main degrees of freedom, the curvature of input/output faces and the lens thickness. When designing an achromat you have even more degrees of freedom, there are the input/output curvatures of each optical element, the thickness of each optical element, the spacing between them, and the material they are each made of, which allows the lens maker even more freedom. With an ashpere the lensmaker is no longer constrained to using spherical surfaces, so there is a virtually infinite number of degrees of freedom (a typical asphere will have about 10 coefficients that determine the shape of the surfaces).

You can try playing with OSLO (a limited edition is free for students) http://www.lambdares.com/oslo-university-program which will directly give you plots of the lens performance for different optical designs.

[kecked]

That was very helpful thank you

[Laser57]

I found a large 12 inch diameter bi-convex lens with unequal curves on each side I've been eyeing to use as a large beam expander lens, but from what I've seen, beam expander lenses are usually plano-convex. Being unable to find large plano-convex lenses very often, at least, for a price I can afford, I'm researching this subject myself and appreciate the above explanation regarding best form. Only one question left I could use some help with, what do you think of the unequal curves on each side, when using as a beam expander, a problem or a help? Unfortunately, I don't have any more information than this on the lens other than a link I can send, if requested on PM. Thanks.

[planters]

Krazer puts it well.

The issue of aberration with these different lens designs is very dependent on focal ratio (as opposed to focal length). Once the focal ratio (beam diameter not optic diameter/focal length) becomes smaller than 1/10 the aberrations become very small and the loss or beam quality due to defocus, inherent laser divergence etc will become more significant. The effect of this ratio increases as it becomes lower and to the second power, ie 1/5 will have 4x the aberrations of 1/10 and the effects of misalignment and defocus also increase at this same rate.

An interesting property of these lens designs is how you orient the lens vs the source. You can place any of these lenses (except the symmetrical bi-convex lens) with the flatter or the more curved surface toward or away the collimated vs the expanding, uncollimatad beam. This can be used to add or subtract spherical aberration from the beam.

Remember, the highly divergent beam exiting a laser diode is not without aberrations prior to striking this lens and so, it is not necessarily the best thing to use a lens with the least spherical aberration. You might want to counter this aberration by choosing and orienting the lens to add a compensating spherical aberration. In one of my videos, I believe I mentioned that the cylindrical expansion optics could be oriented to minimize the far field spot by flipping the orientation of the negative lens. This is another reason that the use of a cylinder expansion pair can be useful (compared to a prism pair). The beam exiting a diode has substantially different divergences in the fast vs slow axis and we are almost universally collimating this beam with a rotationally symmetric lens. The aspherical correction has to be a compromise. The cylinder pair gives us an additional degree of freedom to allow us to minimize spherical aberration in both axes.

Once a beam expander exceeds 100 mm in diameter, it is probably worth looking at a reflective design. Astronomical telescopes can make excellent beam expanders.

[catalanjo]

I agree ...many thanks Krazer!

An interesting property of these lens designs is how you orient the lens vs the source. You can place any of these lenses (except the symmetrical bi-convex lens) with the flatter or the more curved surface toward or away the collimated vs the expanding, uncollimatad beam. This can be used to add or subtract spherical aberration from the beam.....optics could be oriented to minimize the far field spot by flipping the orientation of the negative lens.

That's what I meant by "eminently practical" !

Cheers