Overview
The flashlight aperture test is an easy and direct way to determine the actual working aperture of an optical instrument which employs a positive eyepiece. Simply set the focus at infinity, shine a flashlight straight into the eyepiece from a distance of not less than 10 eyepiece focal lengths, and measure the diameter of the circle of light emerging out the objective. As long as the edge of the circle of light is reasonably sharply defined (blurred by no more than a millimeter or two), one can be reasonably confident of the result.
Some details to observe for best results:
- Use as compact a light source as possible. A narrow, fairly focused, single-LED flashlight is good.
- For most eyepieces, the 10 focal length rule means an eyepiece-to-flashlight distance of about a foot (30cm) is fine. More can only be better, provided the light intensity is strong enough.
- If in doubt about infinity focus, measure near the objective and at least one objective focal length farther away. Tweak focus as necessary until the two measurements are the same.
- A shorter focal length eyepiece will result in a more sharply defined illuminated circle to measure, but it will be dimmer due to the smaller collecting area of the exit pupil.
- While a straight-on alignment of the light into the eyepiece is desired, one need not go to extremes. A tilt of two degrees--which is not hard to improve upon--results in a displacement of the focused image off axis by only 1mm for a 30mm f.l. eyepiece. Or 0.5mm for a 15mm f.l.
How it Works
Note: In this discussion we will treat light as rays. And we will consider ONLY the case of light from a point--or at least an angularly small--source on the optical axis. There is no need whatsoever to consider off-axis light, as we are only concerned with finding the on-axis working aperture.
A telescope receives light from a distant object as parallel rays entering the objective. These rays are brought to a focus, are then collected by the eyepiece, and thence sent to the eye as parallel rays. This is called the afocal configuration. Parallel light in, parallel light out. The diameter of the light bundle emerging is smaller than that entering by a factor equal to the magnification. For example, if the magnification is 10X, the emerging light bundle is 1/10 the diameter of that entering. This emerging light bundle defines the exit pupil diameter.
Turn the telescope around, and the very same thing holds true. Parellel light enters the eyepiece, is brought to a focus at the same point in common with the objective's focus, is collected by the objective, and then sent out the objective as parallel rays.
The flashlight aperture test capitalizes on this property of the afocal instrument. The very same obstructor which might limit the aperture when light enters the objective is the one and same obstructor which will limit the light when passing through the system in reverse. So simple! (And because the 'diagnostic probe' is the light bundle which is brought to a very tiny, near-point source at the focus and on-axis, there is no need to consider the locations of the entrance and exit pupil.)
A compact, single-LED flashlight, while not a point source by any means, is quite adequate. That's because the eyepiece's relatively short focal length brings the image of the light at the focus down to a pretty small size. Not as tiny as optimal, but small enough. The more compact the light, and the farther it is from the eyepiece, and the shorter the eyepiece focal length, the smaller the image at the focus.
Why strive for tiny? The more minute the image at the focus, the less blurred the shadow edge produced by an obstruction and hence the more reliable the measurement. You know you're doing pretty well when the illuminated circle of light has an edge which is blurred by less than 1mm.
The Schematic Diagram
A simple telescope is represented, objective on the left. The eyepiece is shown inside a focuser tube, the latter of which has a set of three interchangeable baffles, or glare stops, installed at the front (left) end. For our purposes, at any one instant only one of these baffles would be in place; you must imagine the other two being absent. No OTA tube wall is represented, as this is of no real import.
Light from our flashlight enters the eyepiece from the right. The rays are drawn parallel, as though the source were extremely distant. In reality these rays would be slightly divergent, like a *very* much more gradual version of the yellow rays. This slight divergence will move the eyepiece focus a *wee* bit closer to the objective, but not nearly enough to make a measureable difference in effective aperture. I mention this only to be pedantically correct. Now you can put this effect out of your mind for the moment (until we get around to those yellow rays, later.)
The full area of the eyepiece eye lens collects light, as represented by the white rays. The outer portion of this extra wide light bundle ends up illuminating parts of the inside of the instrument, such as the focuser tube or diagonal. Now we successively delineate the light bundles which are passed by the three interchangeable baffles, from widest (biggest opening) to narrowest.
The wider baffle passes the bundle contained by the blue rays. Being 'oversized', in the sense of allowing the full aperture to be used for more than just on-axis light, this large baffle allows some illumination of the inside of the scope near the objective. The important thing is that there is no restriction on the on-axis aperture (or even out to some off-axis angle.)
The mid-sized baffle passes the light bundle within the green rays. This baffle is just large enough to allow the full aperture to be utilized, and so we see no reduction in aperture. In normal use, on-axis light passing through the full aperture will be passed on through the system, emerging as a non-restricted parallel bundle whose diameter equals (indeed, defines) the exit pupil.
The small baffle passes the bundle contained by the red rays. Clearly, the outer annulus of the abjective is not receiving light, and so this baffle restricts the aperture. In normal use, light entering the objective's outer zone is blocked by this baffle. And so the emerging bundle of parallel light out the eyepiece makes for a smaller-than-expected exit pupil.
The foregoing applies when some care is given to assuring that the instrument is set to infinity focus, and that the light source is at least 10 eyepiece focal lengths from the eyepiece. To see why the 10X rule is important, consider what happens when the light is located to close to the eyepiece. The yellow rays illustrate this. A light placed within a couple or few eyepiece focal lengths distant will cause the eyepiece focal length to increase significantly. For example, if the light is only 60mm from a 30mm f.l. eyepiece, the eyepiece f.l. is effectively 60mm. By moving the focused image of the light significantly nearer to the objective, the geometry for any nearby obstructors can alter not insignificantly.
Consider the case for the smallest baffle. At the normal focus position the envelope of the red rays clearly misses the objective's outer edge, with notable aperture reduction resulting. But from the relocated focus point, the envelope of the yellow rays passing through the same small baffle is reaching the objective edge; no aperture reduction!
The same effect arises if the eyepiece is otherwise receiving 'parallel' light, but is physically moved inward toward the objective. And of course the opposite occurs if the eyepiece is moved outward.
And adding yet more uncertainty! The incorrect eyepiece focus point causes the emerging light out the objective to be now not quite parallel (in this example illustrated, it's divergent.) And so at different distances from the objective one gets different aperture measurements. This could be rather significant for a Newtonian, as one is already forced to measure rather far from the primary mirror.
This is a much exaggerated illustration, of course. But by being aware of the relevant factors one can realize higher confidence. Such concerns are more relevant for more compact systems and those of shorter f/ratio, and certainly whenever a restrictor lies rather near the focus. In any event, as pointed out above, there's always a solution. When in any doubt, take measures of the circle of light both near to and far from the objective (or tube front end), adjusting focus until the two measures coincide. That's your working aperture.
The Beam Expanded Laser Variation
After some time pondering on how to minimize the size of the focused light at the focus (so as to achieve a reliably sharp-edged illuminated circle for more accurate measurement), it hit me. Use a laser! These devices emit *highly* collimated beams, more than meeting the requirement of near parallelism for the entrant light. But more importantly, the very fact of the precise beam collimation means an *extremely* tiny image at focus. Perhaps diffraction limited tiny! It's effectively a stellar image.
But how to at least fully fill with light the exit pupil sized region behind the eyepiece? One way is to use a short focal length eyepiece which delivers a sufficiently small exit pupil. Green laser pointers are best for this due to their very high visual brightness. They have beam widths of about 1mm, although I believe there are some which are rather wider. As long as the beam width is at least as large as the exit pupil, the aperture will be filled with light and so opposite sides will cast simultaneous shadows for measurement.
But if one has a narrow beam and no way to make a suitably small exit pupil (as applies to most fixed magnification binoculars), the beam must be made fatter. There are commercial beam expanders, which are really reversed Galilean monoculars of small size, but which typically cost hundreds of dollars. An equally good beam expander is provided by a simple, *cheap* finder scope, e.g., 5X24, 6X30, 7X50, etc. A laser aimed into the eyepiece will send out the objective end a beam of parallel light whose diameter is expanded by a factor equal to the magnification. A 1mm beam comes out of a 6X finder 6mm wide. Now we have a way to fill those bigger exit pupils.
One can set the focus on the beam expander in what you now should be taking as standard operating procedure; check beam width near and far, and adjust focus until congruent.
Another benefit of the laser light's supreme parallelism is that you can place the laser in contact with the beam expander's eyepiece, and place the beam expander's objective in contact with the eyepiece of the instrument under test. Convenient! They could all be taped together in a rigid chain.
In all other respects the technique is the same. But now you will have such supreme sharpness that diffraction effects will be well evident.
The primary purpose of this testing is to quantify the actual working aperture of a system on the optical axis. But nothing says you couldn't shine the light/laser into the eyepiece at other angles than just straight on. It's a useful way to examine how and by how much the system vignettes. Experiment!
The update with the laser is a real gem.
