# What is the dimensions of the smallest object detectable by an optical fiber from a specific distance?

Optical fibers are well-known to observe astronomical objects, say, galaxies, to generate massive spectroscopic surveys. The galaxies are often very far from the optical fibers of a telescope. However, I'm thinking about the possibility of using optical fibers to observe much smaller objects (compared to galaxies) like satellites in much shorter ranges like from earth to GEO orbit.

In particular, given an object at the distance $$r$$ from an optical fiber mounted at the focal plane of a telescope, how big (in terms of dimensions) that object should be to be detectable by the signal coming from the optical fiber? (I couldn't find any related specification in the web. Since I need to use the answer as a part of my research, any cited reference is extremely appreciated.)

• Don't the techniques you describe only apply to fixed objects like distant galaxies? It's not clear to me how one would apply it to moving objects. Could you elaborate on this? – Alex Hajnal Jan 11 '19 at 2:39
• Have a look at the beginning of this answer and see if there are any more specific bits of information you can add to your question. As long as your object is in space, say 100 km or higher, it's at infinity as far as the telescope's focus is concerned. Some math about that in this answer. – uhoh Jan 11 '19 at 4:03
• @AlexHajnal: Each optical fiber is often attached to a specific two degree-of-freedom robotic positioner which can move the fiber in a particular work space. This mechanism is well-established in switching the configuration of a set of fibers from one observation mission to another. – Roboticist Jan 11 '19 at 8:22
• Interesting; I'd only heard of the method using fibers mounted in holes drilled in a fixed plate (with a different plate for each part of the sky being observed). – Alex Hajnal Jan 11 '19 at 8:26
• @AlexHajnal: The modern survey projects, including MOONS, DESI, and the family of SDSS projects, all are being (or have been) developed based on these roboticized fibers. So, you have only a single focal plane (or plate, in your terminology). – Roboticist Jan 11 '19 at 8:31

Assuming you are using single mode fiber, the entrance (mode diameter) is small, usually a few microns (extremes can range from 1 to say 30 microns, but 2-8 microns is common for visible SMF).

The only constraint: you have is to get enough light into that small spot. You can do that with a single lens or convex mirror, a microscope, or a telescope, or even by proximity (hold the fiber so very close to a tiny object that enough light reaches the core, works for certain nanoparticle or biological experiments).

Size of target object: So far I can not think of any constraint on the size of the object. Really the question is how bright the object is and how sensitive the instrument is at the other end. If you have a high-dispersion spectrometer, you probably need a lot more light than if you are doing broadband photometry by counting photons with a photomultiplier.

Object is moving: It doesn't matter if the object is moving or fixed, as long as your optical system can move to track it so that the focused image falls on the core of the fiber. That's simply a mechanical and tracking issue not related to the fiber.

The big advantage of using a fiber is now obvious, you can move your telescope, but keep your measurement instrument somewhere else and fixed, and the flexible fiber will guide the light to it.

## Further background

The trick is to put a very large telescope between the object and the fiber, and to use a robot to place hundreds or thousands of fibers at the focal plane, each at the exact location of a galaxy or a star you would like to collect. This way you can line up the other ends of the fibers along a single slit of a spectrometer and study the spectra of thousands or even millions of objects over time without having to point the telescope to each object one-at-a-time.

1. Multiplicity and configurability (as mentioned above)
2. Flexibility (literally) it allows the telescope and the instrument to be mounted separately and not have to be mechanically aligned and stabilized.
3. Mechanical stabilization of source for instruments: even if the telescope drifts and the object moves slightly with respect to the entrance of the fiber, the physical location of the fiber exit can remain fixed. So tracking errors don't affect the distribution of intensity within the entrance slit (virtual or real) of the fiber and therefore don't cause instrumental spectral shifts.

above: From the astrophysicist Ángel R. López-Sánchez's enjoyable A 2dF night at the Anglo-Australian Telescope

above:: From AAO's The stellar cluster behind Sirius

above: GIF from the video (with exciting music) A 2dF night at the Anglo-Australian Telescope

And if you like that robot then consider the "magic fingers" at the focal plane of the Dark Energy Spectroscopic Instrument:

DESI’s focal plane is designed to sit high atop the Mayall Telescope and to carry 5,000 robotic positioners, each holding a fiber-optic cable. Each of these fiber-toting robots is automatically positioned to fix on a preset sequence of individual galaxies and quasars so that the fibers can collect their light. The movements of these positioners must be carefully choreographed to avoid bumping into one another. The roundish focal plane, which measures nearly a meter in diameter, consists of 10 pie-shaped wedges that are fit snugly together. Each wedge holds 500 robotic positioners. The focal plane also contains sensors and light sources called field fiducials that help ensure the positioners are in proper alignment.

And also these robotic fibers in Australia's TAIPAN instrument at Siding Spring Observatory in North-Western NSW:

• and if you liked the music in the video, here is ten more hours of the Inception horn – uhoh Jan 11 '19 at 3:47
• Some follow-up questions if you please: 1-Is Lens equation accurate from the LEO to GEO range? 2-The math analysis you pointed out in another answer seems like applicable to mirror telescopes not those equipped with fibers and spectrographs. Can you explain how that analysis would be also applicable to the latter case? 3-Since the target object may not be so bright, what if someone uses a multi-channel fiber (say, detecting IR or some other waves from EM spectrum)? Is this considered an advantage or disadvantages in terms of "detecting the target object"? – Roboticist Jan 11 '19 at 9:16
• @Roboticist 1) For an aperture of say LEO to infinity you can use the lens equation to estimate the shift in focal length. For a reasonable telescope the shift will be extremely small (like a micron or probably much less), and this would not produce any measurable difference in your fiber coupling. 2) the spot size is the same no matter if you put a fiber at the spot or the pixel of a CCD. For more on that, try to write a more specific question with some details, and think if you want to ask that here or in Physics SE. 3) I'm not sure what a multi-channel fiber is. There are multi-core fiber – uhoh Jan 11 '19 at 9:25
• That's a pretty complicated field in itself. The problem with multiple normal fibers is that the cladding is so much bigger than the core that you can't get two cores very close to each other, so you loose most of your light between the cores. I think it will be great for you to look for older articles about fiber coupling in astronomy. These days it's extremely complicated, but 20-30 years ago they were just getting started and there may be very detailed explanations and calculations. – uhoh Jan 11 '19 at 9:25