Telescope Reviews: Large-ish ATM binos from SS achromats?

In the binocular forum, we have discussed Amici "air prisms",with phantom roofs, whose reflecting surfaces are 2 mirrors. These seem to be the only way to have an erect and unreversed image with two flat mirrors. Other possibilities involve four or six, the next even numbers. Compound angles are involved. One can read about such angles in crown moulding books, compound miter saw manuals, Machinery's Handbook, etc. I prefer to use 3D vector equations, following Hopkins in Mil Handbook 141 ( available in the binocular forum and/or elsewhere in this website), or in analytic geometry sections of textbooks ( usually found with calculus, but you do not need calculus for this project, though I did use one simple derivative to minimize spacing of the mirrors), whose only prerequisite is trigonometry. For 90 degree overall deviation of the lines of sight, the beamprint on each of the two mirrors is a 60 degree ellipse, which has a 2:1 major/minor axis ratio. The angle of incidence of an axial ray is 60 deg. This should be remembered if the mirrors used have been "enhanced", because the coatings are usually optimized for the 45 deg. incidence of a Newtonian secondary mirror. One configuration is that used by Tatsuro Matsumoto for many years, in which the size of the "prism" varies as the IPD is changed. Refocusing is required after any IPD change, in the scheme he used. Another is similar to the WW II Zeiss IPD for the 25 x 100 and 12x 60, in which one eyepiece moved laterally 2x any lateral motion of the (glass) prism. No refocus is needed. In either scheme any error in the 90 deg. angle of the phantom roof, where the planes containing the mirror surfaces intersect, has the result of image rotation. Tolerances are much larger than those for the roof angle of a glass prism, which if the roof line splits the light cone ( as is usually the case), must be very small to avoid image doubling. I call the split case Mode I, and the unsplit cone case Mode II. Both are illustrated very well in Mil Handbook 141 and a reproduction of one of its figures (mode II) by JCB.

About 10 years ago I wrote an about 20Kb. hp48 program for binoculars using air prisms , following Hopkins in Mil Handbook 141. Among others, JCB contributed to a thread in February about this topic , as did PCad. Search our names for early in this year in the binocular forum for more information. Glenn LeDrew has done similar calculations, not automated, for the compound angles involved in his glass Amici prism binoculars' mechanical components.

And by all means see the entries by Luciano. ( Luciano Jorge Ricci, in Macau). But do not be discouraged by his superb execution of the Matsumoto scheme, using sophisticated machine tools and CAD. I believe that wood , or wood/metal plastics will suffice, especially if one is prepared to do some tweaking to compensate for thermal or other minor effects.

It should be noted that 90 deg. line of sight deviation is only one of a continuum of possibilites, ranging from perhaps 60 deg, with long, narrow mirrors, through 80, 90, 100, 120, ..., up to 180 deg. At 180 degrees, the beamprints are the same as Newtonian 1.414 ellipses, and the compound angles vanish, simplifying design and construction. A 180 deg. deviation of the sight line is convenient for the Zenith region, but involves unusual body positions or perspectives when away from the zenith. One can view , while being in Chile, Australia, etc. , the constellations in a "normal" northern hemisphere orientation, as presented in sky charts.

In all cases, the angle of the phantom roof remains 90 degrees.