Optimal lens spacing in DIY symmetrical duplex

[John MacManus]

In the last year, I have built a few such constructs in plumbing pipe. I determined spacing by trial and error using the projected image on a wall. I wanted to be a little more analytical and so purchased a cheapo double-rod optical bench from Surplus Shed.

I have found that the optimal spacing in a duplet is not as narrow as I’d thought. For example [using a collimated source image] I find that a pair of diam/FL 59/350 mm meniscus elements can start producing a sharp image when 31 mm apart. But this distance can be increased to 69 mm with no obvious deterioration in image quality.

My question is which distance do I chose? Am I correct in presuming that the smaller the distance the better? With little knowledge of optics I can convince myself that the smaller the spacing the less chance there is of overall aberration produced by marginal rays passing close to the central axis.

Any help is appreciated … thanks … John

[Maris Rusis]

My experience with symmetrical two element meniscus lenses goes like this:

On axis image quality is fairly insensitive to lens element spacing.

Wider spacing gives a smaller image circle because of mechanical vignetting.

Closer spacing gives a wider image circle but brings into operation more aberration prone edge zones.

Changing the spacing changes the trade off between aberrations. If you minimise astigmatism you make field curvature worse.

There is no absolute best spacing. You have to decide which optical poison you are prepared to put up with.

For infinity subjects an asymmetrical two element meniscus combo works better; weak element in front, strong element behind the diaphragm. The general principle is the amount light bending at each element should be as similar as possible.

A light yellow filter (minus blue) takes away the nastiest part of the chromatic aberration and dramatically reduces the shift between visual focus and chemical focus.

[John MacManus]

Well Maris, I much appreciate your fact filled reply. I will cogitate.

I like your advice "choose your poison". I have been trying to come up with a test chart to indicate to me the relative content of astigmatism, coma, CA etc to guide my choice of elements. Not happy with anything yet. Sounds like choice of spacing would benefit from such a chart also.

Is your "experience with symmetrical two element meniscus lenses" from studying those in your collection, or in assembling your own.

Thanks again ... John

[Maris Rusis]

Hi John, my background is optics and imaging and I used to be a salesman for Carl Zeiss Jena so I seem to have accumulated a lot of lens elements. It's always fun to try various combinations and look at the images on an optical bench (or a view camera, same thing) in case there is a particularly nasty or beautiful or expressive aberration.

There is no great body of research on "bad" lenses and most experiments are leaps into the unknown. It is possible to mathematically predict the performance of any lens but the numerical results don't really give a worthwhile impression of how the image looks; unless you are mentally good at turning matrix math into pictures.

The hard facts are that to correct all the first order aberrations: field curvature, distortion, spherical aberration, coma, astigmatism, chromatic aberration, flare, and vignetting needs a lens system that offers at least as many independent variables in it as there are errors to correct. In practice the more variables the better.

The simplest lens to "correct" all the aberrations is the Cooke Triplet and even it needs three refractive indices (four if you include air), six curves, three thicknesses, and two spacings. And the correction is good only over a narrow field unless the lens is stopped down a lot.

It is nice to optimise image quality with simple lens combinations but sometimes I think it is more fun to make them as bad as possible and see what happens.