The main purpose of this document is to present the utility, coupling concepts and preparation tips of optical fibres for amateurs in astronomical astronomy. For a detailed description of the different types of fibres and features consult this document or the Hetch’s Optics textbook among many others.
An optical fibre is a thin cylinder of dielectric material able to transport light. The beam launched into the fibre is propagated by total internal reflection. A simple thin cylinder of glass acts as an optical fibre, however it is extreme fragile and breaks easily by applying a small bend. A way to reduce this fragility is to coat the rod with a smooth material like acrylic, silicon or polyimide. The fibre is now much more robust and flexible. However, the light cannot anymore transmit inside the fibre since these protective layers have similar or higher refraction index than the rod and therefore no more internal reflection occurs! To solve this problem, the rod (it will become the core of the fibre) is surrounded by a layer of glass (called cladding) with a small refraction index to permit total internal reflection. The refraction index difference between the core and the clad defines the angle (numerical aperture) at which the light can enter into the fibre. The core diameter ranges from few microns up to few millimetres. The length may reach kilometres as in the case of telecommunications applications. For astronomical purposes the lengths are usually smaller than 100m.
Optical fibres may be classified according to the following three:
- Step Index
- Plastic and liquid
- Silica high purity
- Silica Doped
- Incoherent and imaging bundles
- Tapered fibres
- Gradient Index
- Step Index
- Single Mode
- Silica cavity
- Hollow cavity
3.1. Multimode fibres
In a multimode fibre, the core diameter is much bigger than the wavelength of the transmitted light. A number of modes can be simultaneously transmitted. Fibre modes are related to the possible ways the light travels inside the fibre. The primary mode travels parallel to the axis of the fibre and therefore takes the minimum time to reach the end of the fibre. When the incoming beam enters with an angle respect to the fibre axis, the light will follow a longer path and therefore will take longer to reach the end. The number of modes that can be transmitted along the fibre increases with the core diameter.
Multimode fibres may be divided in step and gradient index. In step index fibres the refraction index of the core is constant and the light travels in straight paths. In gradient index fibres the refraction index decreases gradually (parabolic) from the core out through the cladding and therefore the light travels along smooth curves.
3.1.1 Step index fibres
Step index fibres are the most used fibres in fields other than telecommunications. They are relatively cheap and they have the widest range of core diameters: basically from 50 μm up to 2 mm. The material may be plastic, liquid or glass.
Plastic fibres are not wide used nowadays; their optical transmission is poor and the core relatively big (0.5 to 2 mm). The most efficient fibres are made in acrylic and they are mainly used for short length telecommunication networks. In spite of their limited performances, new developments in plastic fibres might open applications in the field of high speed home networks (Gigabit/s). New polymers are being proposed with attenuations approaching the silica fibres.
Most common step index fibres are made in silica glass (core and cladding) because of its high optical transmission in a very broad spectral range. However during the manufacturing of fibres some contaminants remain in the glass which alters its transmission. The most difficult to remove are OH radicals. A large amount of these radicals generate absorption bands in the near IR range (726nm, 880nm, 950nm, 1136nm mainly) but fortunately leave a high transmission in the near UV region that is close to the theoretical limit (Rayleigh dispersion). High purity silica fibres with low amounts of OH contaminants greatly reduce these absorption peaks in the near IR. However, crystalline structures appear while manufacturing preventing a good transmission in the UV range.
Fibre manufactures like Polymicro offer new fibres with high transmission in a very broad spectral range. Curve FVP in Figure 1 shows the typical internal transmission of all silica fibre with high contents of OH radicals. Most all-silica fibres show this transmission since the preform or the bulk of silica where the fibre is pulled come from the same manufacturer (Heraeus mainly). During the manufacturing process, the new FBP fibre is treated in order to substantially reduce the absorption bands in the near IR.
Silica fibres transmit up to around λ = 2 μm while fibres made with fluoride glasses may extend this limit up to 4 μm for few meters. These fluoride fibres are used basically in astronomical interferometers but they are very expensive and fragile. They might be useful in IR amateur spectroscopy in the future.
3.1.2 Gradient index
Gradient fibres are widely used in telecommunications, they are inexpensive and easy to procure. However, as far as we know, never for astronomical instrumentation. There is a common belief among instrumentalists that gradient fibres show low transmission in the blue region. This argument is supported by the fact that these fibres need to be doped to create the axial gradient index, but we have never seen published a transmission curve in a wide spectral range. Most manufactures just announce the attenuation for few wavelengths in the near IR.
We have measured the internal transmission in one of these fibres and found acceptable results for amateur purposes. Figure 2 shows the internal transmission in a standard gradient index fibre of 10 m. If we compare to the step index fibres (Figure 1), the transmission is not very different and in any case totally suitable for amateur applications.
Another argument against gradient index fibres is that most of them are made in only two standard diameters (50 and 65.2 μm). This range of diameters is best suitable for medium size telescopes (2 – 3 m). Therefore the designing capabilities to link other telescopes to spectrographs are limited. In the field of small telescopes these fibres are huge but still they can be used for low resolution spectrographs and/or for bad seeing conditions.
It is also important to point out that the photometric distribution on the fibre output end is very sensitive to any variation of the spot position on the input end and F/# of the incoming beam. Figure 3 shows the output fibre end for different input illumination conditions. We see that his kind of fibre is not a good photometrical scrambler. However, for amateur purposes this feature is not relevant.
About the focal ratio degradation (FRD, see Section 4.4), the refraction index variation in the fibre core practically destroys the information of the input aperture (F/#). Figure 3 a shows the FRD measurements in a 3 m gradient index fibre. If an F/2.3 beam is injected into the fibre, 80% of the flux (relative to the total flux emerging from the fibre) will be collected inside an F/2.3 output beam. For an input-output F/5 beam, the relative efficiency is only 38% ! Therefore this type of fibre is only useful for very fast apertures ! (< F/4 ). In order to couple it to a telescope with apertures lower than F/4, a focal reducer lens is mandatory.
Our advice for amateur applications is to use the graded index fibres for testing purposes or temporary solutions.
3.1.3 Incoherent and imaging bundles
A big number of fibres may be assembled together in a random or coherent way. The random or incoherent bundles are widely used for illumination purposes. The coherent bundles are used to “transport” images in places where the accessibility is difficult like endoscopes in medical applications. In astronomy the coherent bundles are used in the following cases:
- Field acquisition and guiding in multi-object spectroscopy,
- Integral Field Spectroscopy and
- Image slicers
A popular application of fibres in astronomy is to observe simultaneously a big number of stars by placing the fibre input-ends on the focal plane of the telescope. Each fibre needs to be precisely placed in front of individual stars. The fibres may be inserted in a drilled plate or attached to the plate with magnets. At the output, all fibre ends are assembled together on a line to form the slit of the spectrograph. In this case the spectra of all stars are recorded in one shoot. The plate may be precisely drilled in advance to the observations or in the case of the magnets, they can be placed with high accuracy with a robot, for example. At the telescope, the problem is to centre or align the stars in front of the fibres. This can be done with fibre imaging bundles to “see” some reference stars in the field of view and centre them inside the fibre bundle. For example, in the case of the ESO instrument FLAMES, 4 small dedicated coherent bundles are deployed on reference stars inside the field of view. The telescope is moved in such a way that the reference stars fall on the centre of the 4 coherent fibre bundles.
In Integral Field Spectroscopy, the individual fibres are distributed in a two dimensional array. Each fibre end takes the flux of just a portion of an extended object (e.g. galaxy). At the output, all the fibre ends are aligned on the slit of the spectrograph. In this way, the CCD records spectra point by point of the extended object according to the fibre array. Analysing all the two dimensional spectra of the whole object, astronomers may draw, for instance, maps of radial velocities and deduce the movement of the different parts of the galaxy. They can also analyse the distribution of chemical composition in the observed object.
The image of the galaxy can be placed directly in front of a compact bundle of fibres. The fibres can be arranged in a rectangular or hexagonal (honey-comb) array. Since the fibres have a cladding, the cores take just a small portion of the object. The entire object surface between the cores is lost. The best bundles where the fibres have a very thin cladding and arranged in a honeycomb configuration provide a packing ratio (the flux acquired by the cores against the total flux) between 50 and 60%. A way to optimize the packing ratio is to use an array of micro-lenses in such a way that most of the incident flux on the lens is transmitted into the fibre. Figure 4 shows this concept. An array of micro-lenses is placed just in front of the focal plane of the telescope. The fibre ends are put on the focal plane of the individual lenses. The image of the pupil of the telescope is then on each fibre. Most of the flux arriving on the individual lens is transmitted into the fibre. Light losses due to reflections, absorption, aberrations, vignetting by interstices and positioning misalignments must be added.
An Image Slicer is based under the same principle as the IFU, but its purpose is to increase the resolving power of the spectrograph instead. The objects to be observed are no more extended sources but stars. The individual fibres aligned on the slit of the spe4ctrograph provide the same spectrum. All individual spectra recorded on the detector are summed up perpendicular to the dispersion in order to increase the signal to noise ratio. Nowadays, these fibre image slicers are not used anymore in professional astronomy. They are replaced by much more efficient slicers using prisms or stacks of plates.
In amateur astronomy some users still insist to use image slicers with bundles of fibres. As explained in Section 4.4, already the smallest commercial fibres (50 μm core diameter) have a huge projection on the sky for small telescopes. So, there is no need to use additional fibres! We would discourage to use them at all:
• The cores are not side-by-side but separated by a significant thick cladding, so the best packing ratio (amount of output effective flux) is between 40 and 50%. Not interesting!
• For small telescopes usually opened to around F/10, the plate scale or the sky aperture at the focal plate (microns per arcsecs) is very small (in the order of 20 μm/arcsec). A fibre shoulde work at fast apertures (<F/4), therefore a 50 μm fibre at F/3 covers already many arcsecs and it is large enough to catch most of the star flux without need to add more fibres around.
• In addition, 50 μm aperture is relatively big to achieve a high resolution spectroscopy
3.1.4 Tapered Fibres or Tapers
Tapers are optical fibres where the core diameter changes gradually along the fibre (Figure 5). They are mainly used to couple high power laser beams. In astronomy they can be used to couple the telescope beam to the spectrograph with the aim to reduce the FRD. It is an attractive alternative to lenses since there are not alignments and reflection losses. However, laboratory measurements show low efficiencies and therefore tapers are not useful. Coupling properties are described in Section 5.2.
3.2. Single mode fibres
In a single mode fibre, the core diameter is reduced to few wavelengths of the incoming light. For example for a beam with λ = 0.55 μm, the core diameter should be of the order of 4.5 μm. Under these circumstances, the core is so small that only the primary mode can travel inside the fibre. Given the wave propagation of the light inside the cavity, there is no way for the light to take longer optical paths that the wave travelling on the axis. This is the reason why single mode fibres are used in telecommunications to deliver high baud rates: the width of a short single square light pulse entering into the fibre will enlarge less in a single mode fibre that in a multimode one. In a multimode fibre the different modes travelling “slower” will spread the pulses.
In astronomy single mode fibres are used basically to generate interference between beams coming from 2 or more telescopes. Using mathematical algorithms the morphology of the observed object can be deduced. For a more detailed description on interferometry theory with single mode fibres consult this link.
3.3. Photonic fibres
In photonic fibres the transmission of light is guided by a number of cavities around the core. The core may be made in glass or even an air cavity! These are new fibres on the market and for the moment (2008) their performances are still under the requirements for astronomical applications.
The very new Photonics Crystal Fibres (PCFs), also known as “holey” or “micro-structured” fibres, are being studied in astronomical laboratories as a new generation of optical links between telescopes and instruments. They show a structured lattice of holes surrounding the core which can be either empty or solid. This structure obliges the core to act as a cavity where the light is confined and transmitted. In spite of the theoretical advantages the present performances of these fibres are below the “standard” fibres.
3.4. Choice for amateur spectroscopy
Following the acquired experience using optical fibres in professional astronomical spectroscopy, the most appropriate fibres for amateur applications would be the multimode, all silica, step index, high OH radical fibres. They have the most appropriate transmission in a wide spectral range (for less than 10 meters, the spectral range extends from 300 nm up 1.8 μm), they are relatively inexpensive and the choice of standard core diameters meets most of the user requirements.
*European Southern Observatory, Karl-Schwarzschild-Str. 2, 85748 Munich, Germany
Types of optical fibres by CAOS group is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 3.0 Germany License.
Based on a work at spectroscopy.wordpress.com.