Monthly Archives: August 2011

Musing

The Optics of Camera Lens Stacks (Program)

In another post, I discussed the mathematical calculation of optical parameters for a configuration of stacked lenses and camera components. As is evident from the example worked out there, the procedure is somewhat tedious. Instead, it is better to spend twice the time writing a program to do it. Fortunately I already did this and offer it to you, gentle reader, to use and criticize. I expect no less than one rabid rant about some aspect that doesn’t pedantically conform to the IEEE standard. This is working code (and has been checked over and tested to some extent). I use it. However, it is not commercial grade and was not designed with either efficiency or robustness in mind. It is quick and dirty – but graciously so.

Think of this as a mine-shaft. You enter at your own risk and by grace of the owner. And if you fall, there won’t be non-stop human interest coverage on 20 TV channels as rescue workers try to extract you. That’s because you’re not a telegenic little kid and this is a metaphor. Rather, you will end up covered in numeric slime of dubious origin. But I still won’t care.

All this said, I do appreciate constructive criticism and suggestions. Please let me know about any bugs. I don’t plan to extensively maintain this program, but I will issue fixes for significant bugs.

The program I provide is a command line unix (including MacOS) utility. It should be quite portable, as no funky libraries are involved. The program can analyze a single user-specified configuration or scan over all possible configurations from an inventory file. In the latter case, it may restrict itself to configurations accessible using the included adapters or regardless of adapter. It also may apply a filter to limit the output to “interesting” cases such as very high magnification, very wide angle, or high telephoto.

The number of configurations can be quite large, particularly when many components are available, there are no constraints, and we account for the large number of focal/zoom choices for each given stack. For this reason, it is best to constrain scans to a few components in an inventory (by commenting out the components you don’t need). For example, if one has both 10 and 25mm extension tubes then try with only one. If this looks promising, restrict yourself to the components involved and uncomment the 25mm as well.

Either through the summary option or the use of a script to select out desirable configurations, the output may be analyzed and used for practical decisions. For example, if a 10x macro lens is needed and light isn’t an issue then a 1.4X telextender followed by a 200mm zoom followed by a reversed 28mm will do the trick. It will have a high f-stop, but if those components are already owned and we don’t need a low f-stop it may be far more cost-effective option than a dedicated ultra-macro lens (there aren’t any at 10X, but a 5X one is available).

For simple viewing of the results, I recommend the use of my “tless” utility. This isn’t a shameless plug. I wrote tless for myself, and I use it extensively.

Go to Google Code Archive for Project

Musing, Notes

The Optics of Camera Lens Stacks (Analysis)

This first appeared on my tech blog. I like to play around with various configurations of camera lenses.  This partly is because I prefer to save money by using existing lenses where possible, and partly because I have a neurological condition (no doubt with some fancy name in the DSM-IV) that compels me to try to figure things out. I spent 5 years at an institute because of this problem and eventually got dumped on the street with nothing but a PhD in my pocket.  So let this be a warning: keep your problem secret and don’t seek help.

A typical DSLR (or SLR) owner has a variety of lenses.  Stacking these in various ways can achieve interesting effects, simulate expensive lenses (which may internally be similar to such a stack), or obtain very high magnifications.  Using 3 or 4 lenses, a telextender, a closeup lens, and maybe some extension rings (along with whatever inexpensive adapter rings are needed), a wide variety of combinations can be constructed.  In another entry, I’ll offer a companion piece of freeware that enumerates the possible configurations and computes their optical properties.

In the present piece, I examine the theory behind the determination of those properties for any particular setup.  Given a set of components (possibly reversed) and some readily available information about them and the camera, we deduce appropriate optical matrices, construct an effective matrix for the system, and extract the overall optical properties – such as focal length, nearest object distance, and maximum magnification.  We account for focal play and zoom ranges as needed.

The exposition is self-contained, although this is not a course on optics and I simply list basic results.  Rather, I focus on the application of matrix optics to real camera lenses.  I also include a detailed example of a calculation.

As far as I am aware, this is the only treatment of its kind.  Many articles discuss matrix methods or the practical aspects of reversing lenses for macro photography.  However, I have yet to come across a discussion of how to deduce the matrix for a camera lens and vice-versa.

After reading the piece, you may wonder whether it is worth the effort to perform such a calculation.  Wouldn’t it be easier to simply try the configurations?  To modify the common adage, a month on the computer can often save an hour in the lab.  The short answer is yes and no.  No I’m not an economist, why do you ask?

If you have a specific configuration in mind, then trying it is easier.  However, if you have a set of components and want to determine which of the hundreds of possible configurations are candidates for a given use (just because the calculation works, doesn’t mean the optical quality is decent), or which additional components one could buy to make best use of each dollar, or which adapter rings are needed, or what end of the focal ranges to use, then the calculation is helpful.  Do I recommend doing it by hand?  No.  I even used a perl script to generate the results for the example.  As mentioned, a freeware program to accomplish this task in a more robust manner will be forthcoming.  Think of the present piece as the technical manual for it.

Read the Paper (PDF)