5. Linking a telescope to a spectrograph through an optical fibre (Part II)

5.3   Field acquisition (fibre viewer)

When observing with a telescope linked to a spectrograph through an optical fibre, the first problem you are confronted is the way to place the image of the star exactly in front of the fibre input end. How to do it? How to be sure that the telescope beam is properly launched into the fibre? The purpose of this section is to show and describe the most common opto-mechanical configurations to achieve this goal. We discuss the advantages and drawbacks of each of them as well.

Figure 23 shows 5 principles:

  1. A reflective pinhole placed just in front of the fibre entrance: a) to g)
  2. A beam-splitter to bring simultaneously the image of the star and the fibre end into a viewing camera: g) to i)
  3. A micro-mirror or the “negative” version of 1: j)
  4. Backwards viewing of the fibre: k)
  5. Coherent fibre bundle: l)

Most professional observatories choose the principle 1 and occasionally the 5. Principles 1 and 2 contain a number of variations which are described below.

Figure 23.  Optical layouts to monitor the image of the star on the input optical fibre end

a)     Fibre end in front of a pinhole-mirror

An inclined reflective pinhole is placed just in front of the fibre end. The fibre is hold by a commercial standard ferrule or a dedicated support. The telescope beam is reflected by the mirror-pinhole to a viewer camera (or an eye-piece for visual inspection) in order to check the position of the star with respect to the pinhole. In this figure and for practical reasons, a second mirror is used to send the telescope beam perpendicular to the telescope axis. This secondary mirror helps to put the pinhole at small angles in order to reduce the defocus of the star when it is out of the center. The image of the star practically disappears from the field of view when it falls into the hole. When the star is on the fibre, you will notice a small black dot in the centre surrounded by a corona. The intensity of the corona depends on the seeing conditions, hole diameter and sensitivity camera settings (including those from your eye).

Figure 24 shows a picture of a pinhole plate inclined of 10º and a secondary mirror inclined of 35º to send the telescope beam to a viewer camera. The inclination of the pinhole should be as low as possible in order to reduce the vignetting on the fibre end (see Appendix 1). For high inclination angles, the surface of the pinhole is focused on the viewer camera only on a line passing on the hole defining the rotation axis. This high defocusing is sometimes confusing when proceeding to place the image of the star in front of the hole.

Figure 24. A circular 10 mm diameter nickel plate with a 100 μm pinhole in the middle. The thickness of the plate is 50 μm

The diameter of the diaphragm matches exactly the fibre diameter. The mirror-diaphragm can be drilled in a thin plate made by a reflective metal (nickel, steel, aluminium, etc.). The plate thickness has to be smaller than the hole diameter to reduce the “tunnel” vignetting effect (see Figure 25 and Appendix 1).

Figure 25. Vignetting by “tunnel” effect

In spite the concept of placing a pinhole in front of a fibre end is quite simple and straightforward there are a number of difficult problems to overcome if the user does not possess the skills and equipment:

  1. This configuration is not suitable for input beams with apertures faster than F/5 because the focal ratio degradation (FRD) may be unacceptable (an F/3 beam is “faster” than an F/5, more information here).
  2. The procurement of the pinhole. Standard pinholes for laser spatial filtering may be used. They are relatively cheap and they are offered in standard diameters which might be close to your requirements. However, most of them are not “mirror” reflective and they should be polished before installation. Polishing of thin metallic plates is not an easy task, deformation of the plate may occurred.
  3. Laser pinholes are made in thin metallic plates but for small pinhole diameters (50 μm) the thickness may be a concern. The depth of the hole may be a source of high vignetting. We will estimate this “tunnel” effect later (Figure 25). On the other hand, if the plate is very thin, the surface is not rigid and thus not flat. The pinhole acts as a “mirror field” but if the surface shows high bends, the reflective beam can be vignetted by the optics of the viewer camera
  4. There are pinholes made on aluminized glass plates which they look as a perfect mirror with a non aluminized hole in the centre.   The vignetting by the tunnel effect is null and they are very handy. The problem is that most of them they have to be coated with an antireflection layer on both sides of the plate. Otherwise there is a light looses of 8% (4% per surface due to Fresnel losses). On the other hand, the glass surface not aluminized generates a ghost on the fibre viewer camera making the acquisition and guiding difficult. Finally they are in general quite expensive. A solution to reduce the ghost effect would be to use microscope cover object glass plates as substrate.
  5. There are also thin glass plates with a drilled hole in the middle. See for example the “glass apertures” made by Lenoxlaser. In these plates the fibre is exposed directly to the image of the star like in the standard pinholes. However there are two drawbacks: they are not aluminized and the thickness of the plate create some vignetting.
  6. Commercial connectors (SMA or FC) cannot be directly used provided that the fibre protrudes the ferrule to reach the pinhole. This operation implies a careful polishing of the fibre out of the ferrule
  7. An accurate X-Y translation stage or similar device should be used to centre the pinhole with respect to the fibre
  8. The diameter of the pinhole has to be close to the one of the fibre core. If smaller you will definitively loose flux entering into the fibre. However, the hole can be a bit bigger than the fibre provided that the fibre is well centered and that the seeing is bigger than the hole diameter. Otherwise the coupling efficiency drops because you will not able to know if the star falls on the fibre end. For instance, if the pinhole is twice bigger the fibre core and the seeing is very good, comparable to the fibre, the viewing camera (or your eye) will not be sure if the star is on the fibre or between the pinhole and the fibre. If the seeing is high equalizing the pinhole diameter, you can easily control the positioning of the star in front of the fibre.

In item 5, commercial connectors can still be used provided that the ferrule is cut on the side in such a way that the fibre can reach the pinhole. In Figure 26 the fibre has been mounted in a standard FC connector. The ferrule has been rectified to match the inclination of the pinhole. The FC connector has a mechanical reference that ensures to place the ferrule inside the plug always with the same orientation. However, there are still two problems with the commercial ferrules:

Figure 26. Fibre viewer with a pinhole on a fibre mounted on a FC connector which has been rectified to match the pinhole angle

First, most standard connectors (SMA, FC, ST, etc.) have a ferrule with internal diameter of 125 μm. If the external diameter of the fibre (cladding or buffer) does not have this diameter, the fibre core is not centred with respect to the ferrule. Consequently the ferrule cannot be used as a mechanical reference. Second, the fibre may be slightly bent inside the ferrule and therefore the axis of the fibre may be a bit inclined with respect to the ferrule axis. This parallelism error may affect the direction of the light beam entering into the fibre and therefore increasing the FRD (Figure 27).

Figure 27. Parallelism error between the fibre and the connector axis.

Now, if you do not have a dedicated pinhole but instead, the ferrule you want to use is metallic and matches properly the fibre diameter, you can still use it as a mirror if it is properly polished. For that, you cut the ferrule with an angle together with the fibre (Figure 28). Then you polish the end in the standard way to get the fibre glass well polished and the metal ferrule as a mirror.

The polished ferrule acts now as a mirror avoiding the pinhole. The diameter of the ferrule is small but a second reflective surface can be used to enlarge the “mirror” area. This configuration is quite attractive and inexpensive provided the fibre matches the ferrule hole.

The drawback of this solution is that the optical axis of the fibre cannot be anymore aligned parallel to the telescope axis. By the fact that the glass surface of the fibre is now inclined with respect to the fibre axis, the incoming telescope beam has to be adjusted according to the Snell refraction law in such a way that the transmitted beam be parallel to the fibre axis. Figure 28 shows a practical example where the fibre and ferrule have been cut and polished to 10o with respect to the original ferrule surface (perpendicular to the fibre axis).

Figure 28. A metallic ferrule containing a fibre has been cut an polished at 10o with respect to the fibre axis.

In order to avoid an increase in focal ratio degradation, a light ray coming from the telescope axis has to be refracted along the fibre axis. This can be done by tilting the ferrule-fibre of 15o (not 10o ). In this particular example we have assumed an index of refraction of the fibre glass of around 1.5. For small angles the Snell law can be approximated to a linear function (øi = nør).

b)     Fibre protrudes the pinhole-mirror

As shown in the previous case, the reflective pinhole must be as thin as possible to avoid vignetting by the wall. It should have the same diameter or a bit larger than the fibre core and it must be precisely put in front of the core. A trick to release these three constraints is to use a bigger pinhole and pass the fibre through it. In this case, the star must not be focused on the pinhole level but at the fibre end. When the star slightly shifts from the fibre end, the light rays from the star are reflected directly to the eye-piece or camera to indicate that the star is out of the fibre. The fibre length (l) protruding out of the hole is related to the telescope aperture (F/#) and the diameter of the hole (ø) by the following equation.

l= \varnothing \cdot F/\#

Figure 29.shows a prototype with 6 fibres protruding from two polished aluminium “jaws”. Proper grooves were engraved on two aluminium blocks to place the fibres. The exposed faces of the blocks were hand polished.

Figure 29. Up: fibre end out of the mirror plane. Down: detection of the star when it shifts out of the fibre end

Now the problem is to ensure the right focusing of the star in front of the fibre end. One way is first to focus the star at the level of the pinhole with the aid of the eye-piece or camera and then shift the entire fibre head along the telescope axis exactly by the length of the protruded fibre. This can be achieved by mounting the nose of the head connecting the telescope inside a cylinder with 2 mechanical positions (Figure 30).

Figure 30. Mechanics (Lens Holder) to withdraw the fibre head by the length of the protruded fibre

c)     Projection of the telescope pupil on fibre end with a micro-lens

The principle of this configuration has been already described in Section 5.1.3. The fibre end is placed just on the image focal plane of the lens (Figure 31). Since the telescope pupil is very far away in relation to the focal length of the lens (< 1 mm), the image of the pupil is projected on the fibre end. In order to avoid additional FRD, the image of the star must be placed on the object focal plane of the lens. Under these circumstances, the system behaves as a telecentric configuration for any point of the star. This configuration has been used in many fibre links in professional observatories and shows a number of advantages:

  1. Usually the required lenses are very small (less than few millimetres). The whole assembly might be very compact and light
  2. When a so-called “rod lens” is used[1], the lens may be glued directly in front of the fibre. Two air-glass surfaces are eliminated and therefore the optical transmission is increased (left side of Figure 32)
  3. Gradient index lenses (GRIN) may be used. Their standard focal lengths may be close to the required in particular telescope-to-fibre cases. The 0.25 pitch type lenses have their focal planes on the bases of the cylinders and therefore they may be glued in front of the fibre as well. They are usually cheaper than the rod lenses (Right side of Figure 32)
  4. Usually the glue (Norland NOA 63, or Epotek 301) used to cement the lens against the fibre has a refraction index quite close to the glasses, therefore the polishing quality does not need to be excellent, some scratches and digs are permitted
  5. A rod lens may be made with broad band transmission glass like UBK7 allowing a wide spectral range

[1] A rod lens is a plano-convex lens where the thickness of the lens has been extended in such a way that the image focal plane coincides with the flat surface.

Figure 31. A rod lens glued to an optical fibre end

Figure 32. Left: A rod lens glued directly in front of the fibre input end. The length of the lens is 1.5 mm and its diameter is 0.8 mm.  Right: GRIN lenses in front of two fibre ends, one for the star and one for the sky (sky subtraction).

However there are also drawbacks:

  1. As said before, the rod or GRIN lenses are very small (no bigger than 2 or 3 millimetres) and very difficult to handle. They must be positioned in front of the fibre with an accuracy of few microns. Therefore they require dedicated skills, sophisticate tools and alignment equipment (micro-metric translation stages, microscope, micro-holder for the lens, etc.)
  2. Custom rod lenses are expensive and are so small that it is easy to lose them when manipulating
  3. GRIN lenses are relatively cheap but they offered in given focal distances which not always match the fibre diameter and telescope aperture
  4. Most of GRIN lenses do not transmit below 400 nm (Figure 33). However, Grintech company makes lenses extending the transmission spectral range down to 320 nm !
  5. The assembled fibre end is very fragile

Figure 33. Total transmission of GRIN lenses. Top: Selfoc. Bottom-left: GRINTECH Ag-lens. Bottom-right: GRINTECH Li-lens

d)     Projection of the star on the fibre with a single mini-lens

A lens (not necessarily small) projects the image of the star on the input fibre end according to the thin-lens Gauss equation:

{1 \over f} = {1 \over {d_f}} + {1 \over {d_t}}

where f is the focal distance of the lens, df the distance of the fibre end to the lens and dt the distance of the lens to the pinhole.

A simple lens can be used, but a doublet is preferred to reduce the aberrations increasing the coupling efficiency to the fibre.

The aperture of the beam entering into the fibre (F/#f) is given by

F/\#_f = {{d_f} \over {d_t}} F/\#_t

Where F/#t is the telescope aperture. This magnification formula is also valid for the diameters of the pinhole and fibre respectively. The apertures (F/#) must replace the diameters of the pinhole and fibre. For given parameters such as telescope aperture, fibre diameter, pinhole diameter and focal length of the lens, the distances to the pinhole to the lens and from the lens to the fibre can be computed in order to optimize the image of the pinhole on the fibre and the beam aperture in the fibre.

As discussed in Section 5.1.2 this configuration is not optimal since the image of the telescope is not at infinity with respect to the fibre and therefore there is an increase of the FRD. If you choose this configuration it would be advisable to provide a lens with a relatively large focal length (f > 50 mm).

e)     Projection of the star on the fibre with two mini-lenses. The pupil is at infinity

This configuration avoids the increase of FRD given by the previous case (d). Here, the image of the star is directly projected on the fibre input end and the image of the pupil is sent to infinity with respect to the fibre input end. Two lenses may be used to do it. The pinhole (star) is placed on the focal plane of the first lens. The image of the pinhole goes to infinity and the image of the telescope pupil is projected on the image focal plane of the lens. A second lens is placed in such a way that the intermediate pupil is placed on the object focal plane of the second lens. The image of the pupil is sent to infinity but the image of the star is projected on the image focal plane of the second lens. It is at this location where the input fibre end is placed.

This configuration has already been discussed in Section 5.1.2. This layout and the one in c) where the pupil of the telescope is projected on the input fibre end are widely used in many professional observatories.

f)     Reduction of the telescope beam with a lens before the pinhole-mirror (updated 5 October 2020)

In this layout, the image of the star is projected on the input fibre end by using a relatively large lens placed before the viewing system (pinhole, relay lens and camera/eyepiece). A commercial focal reducer lens for Schmidt-Cassegrains may be an option. There are a number of commercial reducers but a popular one is the  F/6.3. This lens is usually adapted to F/10 telescopes. The exit beam is then F/6.3 (magnification = 0.63x). The image quality (mainly driven by chromatic and spherical aberrations) is good enough to couple most of the flux into the fibre. The coupling efficiency depends mainly of the fibre diameter, plate scale of the telescope and seeing variations (go to this link to compute the amount of flux launched into a fibre or a slit given by these parameters). As previously discussed ( see Conclusions in Chapter 4. Characterisation of optical fibres), a fibre working at F/6.3 is not advisable because it still shows a high focal ratio degradation.

Following experimental data, if the fibre works at F/6 (input and output beams) the transmission is reduced by 30% – 40% due to FRD. A reducer with a shorter focal distance is then needed. On the market there are focal reducers with lower magnifications, such as 0.5x or even 0.33x. We do not have experience using these focal reducers, so we cannot confirm if they have enough image quality for an efficient fibre coupling.

As discussed in the solution d), a focal reduce may increase the FRD by the fact that the pupil is not at infinity. However, we have recently studied in some detail this problem and found that the increase of FRD is not significant as soon as the distance pupil – fibre is more than few millimetres. For a reducer 0.63x working at F/6.3, the FRD is less than 1% if the distance fibre -pupil is larger than 50 times the fibre diameter. If you use a 50 μm fibre, the distance must be larger than 2.5 mm!

Let’s check the configuration with an 6.3x focal reducer. We found in the internet that these reducers ahve a focal distance of 230 mm. For a C14 telescope, the nominal back focal distance (bfd is the distance from the edge of the mechanical flange of the telescope to the focal plane) is 140 mm.

When the focal reduced is installed, the bfd becomes 85 mm. It is at this new plane where the fibre end has to be pointed.

As for the optimisation of the FRD, the F/3.3 reducer would be fully appropriate (FRD < 15%). Unfortunately the manufacturers don’t provide the focal distance of their reducers. Taking into account the same telescope parameters, we estimated the focal distance of the 0.33x reducer  to 68 mm. The resulting bfd is around 45 mm. This distance is short but probably enough to place the pinhole and the folding mirror for the viewing camera.

We have simulated the image quality provided by a commercial doublet (Thorlabs AC254-100-A) with f = 100 mm and diameter 25.4 mm to check if it can be used as alternative as a focal reducer. The resulting F number is F/4.2 and the bfd = 55 mm . This aperture (F/4.2) is still appropriate as for the FRD. Following the efficiency measurements, the FRD is between 10% – 15%. The spot diagrams are shown below.

Left side shows the spot diagram for a spectral range of 400 to 700 nm, right side for a 450 – 650 nm range. We can see that the chromatism increases rapidly with the spectral range. However, for a spectrograph working in a restricted spectral range, the doublet is a good alternative to the focal reducers.

g)     A beam splitter and a mirror-pinhole

A metallic ferrule or a pinhole-mirror is placed in front of the input fibre end. The image of the star is projected on the fibre and (if the star is not at the centre) it will be backwards reflected to the telescope. A beam splitter mirror at 45o is then placed above the fibre head to send the reflected beam on an eyepiece or a CCD/web camera. In order to mark the position of the fibre on the camera and consequently on the monitor, the fibre is back illuminated (from the spectrograph). Under these conditions, the star will “disappear” on the monitor when it falls on the fibre.

The big drawback of this solution is the low coupling efficiency to the fibre because the shared reflectivity of the beam splitter. Usually the beam splitters have 50 % reflectivity and 50 % transmission (ideally). This is not a good option since you lose 50% of the flux into the fibre. At the limit, you can use a simple glass plate where the upper surface is anti-reflection coated. The transmitted flux will be at least 94 % (for a single layer of MgF2). However the flux sent to the camera (or eye-piece) will be no more than 4 % !

A way to increase the flux on the camera is to use a 50 – 50 % beam splitter and flip it during the exposure. The mirror may come back to the initial position for few seconds to check the right position of the star in front of the fibre. Alternatively, the telescope guiding can be performed with a second camera and small telescope mounted in a piggy back on the main telescope. The small telescope should have its focal distance close to the one of the main telescope in order to maintain a precise guiding.

h)     A beam splitter or dichroic filter and a flat mirror

In the previous case, a pinhole mirror or a reflective ferrule is compulsory. If you do not have any, you can use a flat mirror instead. This mirror must be placed on the focal plane of the telescope which has been left folded by the beam splitter (or dichroic). The fibre input end has to be placed symmetrically with respect to the beam splitter and mirror. Again, in order to mark the position of the fibre on the monitor, the fibre must be back illuminated to project its image on the camera.

This arrangement requires a careful alignment of the elements to accurately superimpose the image of the star and the image of the fibre on the camera. An inclination error of the flat mirror will produce vignetting to the relay optics. A tilt error of the beam splitter will separate the images of the star and fibre on the camera.

The same problem mentioned in the previous case about the reflectivity of the beam splitter remains here. In addition to the solution to flip the beam splitter during the observation, a dichroic filter can be used instead of the beam splitter. A dichroic filter is a mirror where the light is split in two wavelength ranges. For example all the visible spectral range can be transmitted. Beyond a given wavelength the rest of the spectral range is reflected. For our application, there are dichroics with the cut wavelength is at 700 nm. The visible spectral range is transmitted (~ 90 %) and the near-infrared is reflected. This filter will increase the flux of the star to be observed to the monitoring camera and there is not need to flip the dichroic along the observations.

i)     A beam splitter or dichroic filter and a spherical mirror

This configuration is the same as the previous one but the flat mirror is replaced by a spherical mirror. The projection of the fibre end on the camera is made by the spherical mirror and not anymore by an objective. Note that the camera detector is placed on the centre of curvature of the mirror.

From the cost point of view, this solution is more attractive since the spherical mirrors are cheaper than the objectives (usually a doublet).

j)     Micro-mirror on a glass plate

In this layout, the pinhole is replaced by a very small mirror with the same diameter than the pinhole. It is the “negative” format than the pinhole. The micro-mirror is imaged on the input fibre end by a relay optics (a doublet is an acceptable solution). The field monitoring camera or eye-piece is placed below the micro-mirror. When the star falls on the micro-mirror, its image is projected on the fibre end.

A relative easy way to make such a micro-mirror is to use an appropriate pinhole as a mask during the aluminizing process. The pinhole can be drilled on a thin metallic plate nor use cheap laser pinholes.

Still another solution to make the micro-mirror is to aluminize the fibre end of a small (few millimetres) piece of fibre! It can be glued on a glass plate or hold by a needle.

k)     Fibre end glued on a glass plate (or a band)

The fibre end is directly glued on a glass plate which is located on the focal plane of an eye-piece (or a relay lens of a monitoring camera). This eyepiece (or lens) is inserted in the telescope in such a way that its focal plane falls on the plate surface where the fibre lies.

In order to avoid short bending radius of the fibre (high FRD!), the focal distance of the eyepiece or relay lens has to be greater than few centimetres.

A relevant drawback in this configuration is the careful gluing of the fibre on the glass plate. The glue must not overfill the fibre diameter! Otherwise the excess of glue increases artificially the fibre diameter and reduces the position accuracy of the star in front of the fibre core. This problem remains even if the glue is transparent. Since the glued surface is very small, the set-up results very fragile. It is interesting to note that this idea has been already patented in Germany!

A way to overcome this glue problem is to mount the fibre on a thin band as illustrated in Figure 34. The band thickness must have the diameter of the fibre or less to avoid shadowing of the star.

Figure 34. The fibre input end is glued along a thin band

l)     Coherent fibre bundle

An elegant way to monitor the star in front of the fibre is to surround it with similar fibres. The most appropriate way to arrange the fibres in a honeycomb configuration. It can be just 6 fibres around, but the field of view is extremely small. On the other hand, the distribution of the fibres at the other end must be preserved. A relay lens should project the image of this fibre array on the viewing camera. No pinholes and mirrors are needed. However, iIt is clear that the big problem here is its manufacture!

It is interesting to point out that the fibre positioner of the FLAMES instrument in ESO Paranal Observatory uses this principle for acquisition and guiding purposes (Figure 35).

Figure 35. 19 fibre coherent arrays of the acquisition and guiding system of the OzPoz-FLAMES positioner system

Appendix 1. Vignetting by Tunnel effect

Pinholes introduce 2 vignetting effects: vignetting by the internal wall of the pinhole and additional vignetting when the pinhole is inclined. Figure 36 shows the vignetting created by the wall of a thick pinhole. The image of the star is projected on the left polished surface of the pinhole. We assume that the wall of the tunnel is opaque and that the star has a uniform flat illumination. Taking a single light beam sweeping the field from the centre to the edge, the vignetting will star as soon as the beam touches the rear side of the pinhole.

Figure 36. Vignetting by the wall of a pinhole

In this appendix we define the vignetting by the integrated loss of flux as a function of the field (total contribution). It is zero when all the beams in the field are not obstructed and grows when the residual beams touch the wall (or other limiting apertures).

The amount of flux loss will depend of the thickness of the hole (e), the telescope beam aperture (F/# = F) and pinhole diameter (ø). In Figure 36 the hatched area represents the actual obstructed flux. The relative area with respect to the area of the pinhole is given by (the factor π/4 has been removed):

V = { {(\varnothing +2a)^2 - \varnothing^2 }\over \varnothing^2} \approx {4a\over \varnothing}

We have assumed that the length of the tunnel (e) is smaller than the pinhole diameter (ø) and therefore the quadratic contribution is negligible. Since a = e/2F, the total vignetting is given by:

V \approx {2e \over \varnothing F}

As an example, if you have a 100 µm pinhole with a thickness of 50 µm and your telescope beam is opened to F/5, 20% of the flux will be lost by effect tunnel.

The vignetting is increased when the mirror-pinhole is inclined (necessary to send the telescope beam to the viewer camera). Figure 37 shows a pinhole inclined by an angle α.

Figure 37. Vignetting by the wall of a pinhole when the plate is inclined by an angle α.  ø is the pinhole diameter, η is the small axis of the projection of the pinhole by the angle α and γ is the “eye” aperture.

First, note that there will still be a vignetting even if the plate has no thickness, like in the aluminized plates. The telescope beam will “see” the projection of the inclined circle as an ellipse and the effective area will be reduced by the cosine of the inclination angle. The normalized vignetting contribution will be

V = 1 - \cos \alpha

When the length e of the pinhole tunnel is about the radius of the pinhole (or longer), the main contribution to the vignetting will be done by the tunnel effect and the obstruction created by the overlapping of the ellipses defined by the edges of the pinhole (see the picture on the right side of Figure 37). The clearance defined by the two shifted ellipses looks like an “eye”. Its area can again be approximated to an ellipse. The two semi-axis of the ellipse are close to ø and (ø – e sin α)/2. The normalized vignetting contribution will be:

V = { e \sin \alpha \over \varnothing}

Finally the total vignetting to the three contributions is:

V = { 2e \over \varnothing F} + {e \sin \alpha \over \varnothing} + 1 - \cos \alpha

A rigorous calculus of the vignetting is much more complicate as the sum of individual contributions. However, our purpose is to give an idea of the vignetting magnitude.

Taking our example of a 100 µm pinhole with 50 µm thickness, inclined of 15o and illuminated by an F/5 beam, the vignetted flux will be around 36 % !


  1. In the case of a pinhole made on an aluminized glass plate (e = 0), the vignetting is zero if the fibre diameter equals the minor axis of the projected ellipse
  2. For thick pinholes, the vignetting will be appreciable if the thickness of the plate is around the radius of the pinhole and especially for fast telescope beams
  3. The vignetting will be highly reduced if the fibre input end is inside the “eye” clearance of the pinhole (Figure 38)
  4. In any case and in addition to the vignetting, the coupling efficiency to the fibre may be highly affected if the  pinhole angle is not small and that the “seeing” condition is not very good. Indeed, the image of the star may fall between the fibre and the edges of the hole producing high flux losses.

Figure 38. Projection of the fibre input end on the pinhole


Gerardo Avila*


Carlos Guirao*

*European Southern Observatory, Karl-Schwarzschild-Str. 2, 85748 Munich, Germany

Creative Commons License

Field acquisition (fibre viewer) 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.

$latex l=\varnothing \cdot \frac{F}{#}

$latex l=\varnothing \cdot \frac{F}{#}


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4 responses to “5. Linking a telescope to a spectrograph through an optical fibre (Part II)

  1. Frank Larsen

    Quiestion: I use a classic 12″ F/10 SCT and is trying to make af fiber interface. I will use a standard guide interface consisting of a 4mm thick tiltet firstsurface mirror where I either cut a slit 15-30um wide, a cross of two perpendicular slits or a pinhole Ø30-50um. (The cutting is actually very easy and gives a very high quality and narrow slit).
    My plan is to project the slit/cross/pinhole and thus the airydisc of the star onto the fiber end.

    However I cannot see if e) or f)+relaylense is the better way to do it.

    e) gives the biggest star diameter, biggest trouble guiding (mechanical) and is more expensive because I need two doublets. Small guidefield at F/10 gives some trouble aquiring the object of interrest and extended objects have low brightness. Getting multiple lenses aligned is also somewhat more involved.

    f) gives me smaller star image on the slit/cross and is easier to guide (my normal spectrograph works by this principle). Its easier to find the object and extended objects is brighter and would give more photons through the slit.
    I would take one doublet or an eyepiece to project the star+slit/cross so that the F/# changes to perhaps F/5 – but above You give a hint that there might be trouble getting the image on the fiber to have good enough quality. Is it just the diameter I have to inspect? (can do that by placing a camere instead of fiber!?).
    What about the focallength of the relay lense – and what about the position of the lense. Should it be put where the aperture of the telescope is projected by the focalreducer – ie 140mm behind the slit/cross. seems a bit impractical!? It had planned to use a simple 12mm eyepiece as relay lense.

    So which way is the better one? (It should also be fairly easy to make and align)
    What about using molded aspherics normally used for laser collimation? I buy my stuff from Thorlabs and they have a lot of those. Are they any good for type e) optics?

    the only alternative for me is to use a fiber with steelferrule and polish it at an angle and place it in a block of polished aluminium with a 2.5mm hole. Then work at f/6.6 or even at f/3.3.
    Problem is that I have never polished a fiber and would like to avoid this and just use stock stepped-index SMA terminated fibers.

    Frank Larsen, Denmark

  2. Anu more resources on subject? Im interested 🙂

  3. Anu more resources on subject? Im interested 🙂

  4. Pingback: Linking a telescope to a spectrograph through an optical fibre. Part III |

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