Hello all,
I am glad to see that you guys are well! The white paper by Mr. Cobos on binoculars' collimation is very interesting. I remember reading a previous version of his article more than a year ago. I was very impressed by it. Mr. Cobos' original paper corroborated my findings about the ill-posedness of optical beam steering using a Risley prism pair. It also inspired a new invention in a totally different field (side-by-side double rifles).
Collimation of binoculars by adjusting objective lens positions housed in eccentric rotatable rings causes two fundamental problems:
A- Requires solving an ill-posed inverse problem: It is straightforward to calculate where the optical axis of each objective lens is given the rotational position of each eccentric ring (i.e. forward problem is well-posed). However, the inverse problem of calculating the rotational positions that would produce a desired lens axis position is
ill-posed. This is because the problem does not have a unique solution and, worse, the solutions are unstable. A small change in the required position of the lens center might require a very drastic change in the rotational position of the rings. This is why Mr. Cobos has to rely on a spreadsheet to help solve the problem and even then, it will take multiple iterations to solve the problem.
B- Shifting objective lens axes will destroy internal collimation of each barrel: If each individual barrel is adjusted in the factory such that all the lenses are on the same axis, then any additional shift to the position of the objective lens to achieve collimation between the two barrels will destroy the internal collimation of individual barrels.
The above problems are not faults of Mr. Cobos's method. They are faults associated with the way binocular's are constructed. I wonder if all modern binoculars are collimated by shifting their objective lenses or by shifting their erector prisms? Is there any other way? How do Leica, Swarovski, etc. collimate their binoculars in the factory?
-Omid
Where do I begin to tell the story .... Oops, wrong intro.
I see no way to address this issue without stepping on the toes of a couple of people who I respect immensely and who are, without a doubt, smarter than me.
Omid states: “Shifting objective lens axes will destroy internal collimation of each barrel:”
The word
“will” should be replaced with
“could.”
ANY movement of the objective WILL shift the line of sight. However, considering improvements in the art of lens making, improvements in CNC machining, and the observer’s spatial accommodation—obviously not considered in his calculations—more often than not, this will become a non-issue. Attached is a photo of Eric Magnusson—former Navy OM2—centering the elements of a 3-inch objective from a 1943 Quartermaster Glass. We had to recement the crown and flint elements because optical quality can suffer if the elements are not concentric.
In situations in which there is not enough motion in the eccentric to achieve collimation, there are other simple methods to correct this deficiency.
1) Objective lenses can be swapped telescope to telescope.
2) The objective lens can be turned in 90-degree increments—in its cell—on either OR both sides.
3) Finally, if the above doesn’t work, a tiny shim can be placed between the lip of the inner eccentric ring and the front of the lens. This is certainly not the best way, but in extreme cases, it IS a viable option. By tiny, I don’t mean 1/4 -inch. I’m referring to a displacement of .002-.004-inch. This is on the face of the crown element. However, I have seen places in which a larger shim on the SIDE of the ring would be practical.
By using eccentric rings in the alignment process, you are moving the line of sight
LATERALLY, which means the objective has been removed from causing problems with third-order aberrations which is always an issue with the through-the-body/prism-tilt collimation convention. And while the increase in third-order aberration is a reality. It is usually so slight as to only be a concern for the irrational optical nitnoids who have to have something to worry about. Also, while the collimation of the optics in “Each Barrel” is part of the whole, it usually represents such a tiny part of the overall condition as to be inconsequential, easily fitting into the range of Spatial Accommodation of the most sensitive observer. It’s the line of sight of one telescope to the other and the optical axis that really matters. This may be troublesome for optical postdocs but very rarely is for experienced technicians. Enjoyable binocular images do not originate from the result of algebra or geometry but rather practical knowledge, the right test setup, skillful hands, and sometimes a touch of patience.
Finally, while there are those who find problems behind every bush, the following may be a calming agent:
An exhaustive survey for the Armstrong Aerospace Medical Research Laboratory in May of 1986 revealed in part:
“Indeed, a degree of alignment error unnoticed by, or even undetectable by, one observer may be unacceptable to another.” And ... “Zero optical tolerances and zero for image difference are not practical: they would be too difficult and expensive to obtain and could not be retained in use.”
While my credentials in academic optics are not even a good shadow of those possessed by Omid, having collimated thousands of binoculars, offered contributions to Zemax lens design software, and been an invited speaker on the subject to the optical engineers of SPIE, where I added to the vernacular, I think I have a pretty good handle on binocular collimation.
Rafael:
I have great respect for this man. He has been on the front lines of teaching the basics of the process for years. The problem I see with his work—for me—is all the reading, UNDERSTANDING, setups, calculations, and documentation involved.
His first program took up 31 pages, required the use of a moving sun, not hampered by cloud cover—possibly for days—rain, etc. when a much simpler and more efficient setup with an 8-inch telescope and a handheld, low-power auxiliary telescope was possible. BUT, did that stop him? Nope! He devised a method using auto-collimation and projection. A heavy, expensive, and complicated projection system was also devised by the US Navy in the MK13 binocular collimator. It fell into disuse and for several good reasons. (Mk 13, attached)
Most of my time with binocular collimation has been in a professional setting. Thus, I had to get swiftly to the brass tacks.
But Rafael has been driving like a dedicated 17th-century optician to bring new and useful concepts to all of us. Those who piggyback on his work will learn what they need to about binocular collimation and will undoubtedly make further contributions in streamlining. :cat:
Congrats and keep up the good work, Rafael!
Bill
PS There ya go, Steve.