So in the previous post I came to the conclusion that an objective with forward pupil can overcome the short working distance of macro. The pupil is on the front, outside the lens; so there is no problem in focusing near it.
Where to find an objective with such feature? Pinhole lenses have been tried already, while the wide Zeiss Sonderobjektiver seem unobtainable. But it happens that eyepieces – yes- have this forward-pupil feature, and I found some already waiting for me in my house. Maybe in your house there are some too. Get one, and look through it from the back – at some distance; here is your macro, quite wide angle objective.
Eyepieces are designed to pick up the intermediate image produced by the telescope objective, and project it with a wider angle toward the observer’s eye pupil. Since the eye is external, the eyepiece needs to have its own aperture optimized to stay outside; the free distance between the last lens and the aperture is called “eye relief”, since this distance makes easy for the observer to pick the image. This aperture is virtual, will match the eye’s own physical aperture (iris) and should image the objective’s aperture.
In order to be coupled with the long-focus objective, the eyepiece is designed to be (roughly) telecentric toward the intermediate image; that is a huge boon for using it in a probe setup.
As shown in the illustration, the eyepiece alone can be seen (and used!) as an objective by itself; it is optimized to work at infinity (that makes easy to the eye to observe) but we may stretch it to focus closer; the image will move a little farther, but remains of the same size (telecentric!) and on the subject size, the angle of view is held constant as well. At macro magnification the subject remains at a fair distance, the eye relief plus the focal distance.
The eyepiece can be mounted directly in front of the sensor (bare mount). Although simple, this setup is far from optimal: eyepieces typically have very short backfocus, hence it is practically impossible to focus at infinity; only large magnifications are accessible. Then, the eyepiece does not have a proper aperture stop, so rays are vignetted unordinately; in the centre of the field, a too large aperture is allowed. The situation can be improved by putting an aperture cap in front, like pinhole lenses; if it is in the right place, will not interfere with the field. The backfocus can be shortened by a slimmer adapter or by a camera with shorter flange distance, so the lens can come closer to the sensor, for lower magnifications.
Further improving, a relay system provides much more flexibility. A macro lens is interposed; it picks the virtual image formed by the eyepiece and project it to the sensor. The focus can be controlled by moving the relay lens (and/or the camera); the aperture of the relay is in the right place (“natural” aperture place) and it is imaged in the front of the eyepiece, working as virtual aperture. In front, all working distance is available toward the subject (eye relief + focal distance).
Which eyepiece? Which relay lens? How to mount them?
There is quite a huge choice of those items. There are eyepieces for microscopes, binoculars, telescopes and more. I’ll discuss those for telescopes that are easier to mount. Those are labeled by focal length (in mm) and the angle of view they provide. The fitting is by sleeve, either 1 1/4 or 2 inches and there are several adapters that can be used to mount them with civilized standard threads, like the T2 (M24x0,75). Almost all have have a female filter thread, M28.5×0.6 for the small eyepieces and M48x0.75 for the large ones. Often the sleeve can be screwed out, revealing another thread that with some luck may match one of your adapters. Lacking those metal options, duck tape, glue, cardboard or a 3D printer may step in. Eyepieces are available also with other mounts, like 23 and 30mm sleeve for microscopes, with adapters rarer and more expensive.
Focal lengths range from 2mm to 55mm, and the angle of view from 20 degs (narrow), 50 (normal) and more than 70 (very wide). There is usually a physical field stop that defines the size of the intermediate image; its diameter varies in function of focal length f and the angle of view 2 theta (no distortion approximation; in practice it will be a little bit smaller):
Eyepieces are manufactured almost telecentric; the “almost” depending on the quality and on the fact that they are intended to be coupled with a long but finite lens (the amateur telescope objectives, 500-1000 mm), therefore we expect a small convergence to be designed in. Coupling them with a relay lens at shorter distance will slightly shift the aperture from where it was designed, and some optical aberration may arise, like coma. I couldn’t find anywhere those specifications; you may try your luck and ask a manufacturer for the designed aperture distance! This observation tells us that as relay lens, a long focal lens, at low magnification, should work better than short ones put near. I didn’t test this theory thoroughly, maybe one day. About distortion, the projection is usually rectilinear, with a small amount of barrel, increasing as the angle gets wider.
An ideal setup entails the relay lens working at 1:1 magnification or slightly less; hence it is desirable to have the intermediate image of size capable to cover the sensor (it will be projected on the sensor 1:1), either by filling it (full rectangular image) or inscribed, as a fisheye. Below a table with the diameter values calculated from the formula, in parenthesis a more realistic value that takes into account barrel distortion. Compare those values with the image circle needed to cover a 35mm full format sensor, 43mm, the APS-C (30mm) or MFT (22.5mm).
| Eyepiece type | Normal | Wide | Superwide |
| Angle of view (2 theta) | 50 | 70 | 100 |
| Focal length mm | |||
| 5 | 5 | 7 (6) | 12 (10) |
| 10 | 9 | 14 (12) | 24 (20) |
| 20 | 19 | 28 (24) | 48 (40) |
| 40 | 37 | 56 (48) | 95 (80) |
So, for a full format sensor we need pretty large and wide eyepieces; those are massive instruments that weight over a Kg and cost 1K$; over 29mm of field, the 1 1/4″ fitting is too small and only 2″ is used. MFT owner can rejoy once more. Eyepieces with smaller image circle can be used as well, either by accepting a small image circle, or by increasing the secondary magnification of the relay. This setup may get advantaged thanks to the smaller magnification expressed by the eyepiece, leading to smaller aberrations.
I tried all 7 eyepieces in my possession (cheap to medium) on APS-C sensor, and best results were from a 15mm with 70 FOV; the image circle was a bit smaller but the image sharper overall than the other eyepieces. I don’t own and haven’t tried real luxury eyepieces.
The standard barrel fitting of telescope eyepieces is not really the best mounting interface (unstable and not precisely centered); but comes with the boon of all the fitting accessories available for telescope: adapters, barlow lenses, filters, helicoid focusers, sideview collimators (recyclable as coaxial illuminators), diagonals and elbows. If you think that putting a 90 degrees bend in front of a lens is silly, have a look at the list prices of the Innovision probes! Or you can try to rent the T-Rex.
About image quality, what is the best eyepiece? That is an issue that has been discussed since ages and will be discussed for some more centuries. You can dig yourself in the forum Cloudynights, There are several serious companies, vendors and optical designers dedicated to eyepieces. Basic wisdoms are: all eyepieces, even the simplest, are very sharp in the center of field; all struggle to keep up at the wide angle, and wider models need a more complex (expensive) design. As many other optical product, the image quality increases logarithmically as the price increase (with outliers).
For fast and visual comparison of 9 eyepieces, around the 25mm focal length you can look here and thank this Louis D for his work; the truly “alpha” eyepieces are missing. More resouces on eyepiece are for example Vladimir Sacek, Don of EyepiecesEtc.
Microscope eyepieces have usually a narrower field of view, but small to none barrel distortion; are designed to be conjugate to the microscope tube lens, typically about 200mm, well defined and shorter than a telescope. Some brands have built-in aberrations, to compensate for the objective ones, which may pop up un the photos.
Use of complete telescopes
If you have a binocular and think of dismember it to get an eyepiece, stop! It can be used directly: in fact telescopes are nothing more than afocal tele extenders; or, in the opposite direction, they are afocal wide-angle attachments. Not convinced? Have a look into a binocular from the wrong side, you’ll understand.
The telescope can then be mounted directly in front of a telephoto lens;; an alternative way to see it, is the telescope objective being a diopter, that helps the telephoto focus at the eyepiece’s intermediate image. Of course large telescopes are unpractical to mount and bring on the field; but small monoculars or one tube of a binocular may fit well ; they also provide upright image and internal focusing! Binoculars are labeled by their (angular) magnification (like, 8x), objective diameter (32mm) and real field of view (like, 9 degrees). Used as wide angle attachment, the 8x represent the widening effect (1/8, inverse of magnification!); the objective diameter is the aperture, to be compared with the paired telephoto one (example, 200mm f/4 -> aperture = 200/4); if they match is best, smaller will limit the max usable aperture. The field of view should match the one of the telephoto, so to fill the sensor with the eyepiece’s image. Thus, high power telescopes must be avoided because of their extremely narrow field of view.
Riflescopes are another edition of the monocular; they are interesting as macro objectives because they have very good optics (depend on price) and a special eyepiece a bit narrow but with extremely long “eye relief”, 40mm or more, which will become our generous working distance when doing macro. The crosshair in the image plane of the riflescope will be out of focus and won’t cause problems.
Binoculars and riflescopes are of course an hassle to mount in front of a lens and bring to the field to chase bumblebees; a small monocular glued to a filter thread it is instead quite practical, specially if the telephoto holding it has internal focus.
Half cooked dreams by Giorgio Pattarini 
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