We present here our based prism low resolution spectrograph baptized BESOS or BEst Simple Optical Spectrograph (kisses in spanish). Designed in 2003, the spectrograph was proposed to overcome the  low throughput of our previous instrument LOROS (coming soon to this blog) which was an instrument based on an on-axis dispersion prism obtained from a commercial spectroscope. The total efficiency of LOROS was only 25% in the visible spectral range.  BESOS was built with only two doublets and a prism. This configuration reached almost 87 %  at 620 nm. With such efficiency and low resolution, we expected to measure the red shift of the most bright galaxies and quasars.

In this post we provide a description of the instrument, features, performances and the set of mechanical drawings.

Optical design

The Figure below shows the optical design of BESOS. The description of the elements  is given in the Table below. The prism works at the minimum deviation and for this configuration the incidence and refracted angle to the input and output prism surface is 59.6960º respectively.

Two LINOS (now Qioptiq) doublets were chosen as collimator and objective respectively. An equilateral 60º prism from Edmund Optics was used as disperser. The image quality at 400, 550 and 700 nm is illustrated in the following Figure. The square is 20 μm side. The images for these 3 wavelengths were optimized to have their minimum spot size perpendicular to the dispersion.

Technical data

Technical drawings

All BESOS technical drawing ara available for download in this PDF document:  BesosAllDrawings

This image describe the BESOS assembly with both optical and mechanical components. The only remark worth being mentioned is that the mechanical part 3 – Folding Mirror is made enterily of black anodized aluminium except the inclined surface that has been polished till it achieved the quality of a mirror surface (probably would habe been simpler solution to glue a small mirror).

Gallery

The following photos show BESOS in different configurations

BESOS

SRL camera as detector and a webcam as slit viewer

BESOS ready for observations with SBIG ST-8 and webcam

BESOS at the telescope with SBIG ST-1603ME

Observations

• Mallorca (Spain) .November 2003.  All exposures between 1 and 120 seconds.

“BESOS: a prism spectrograph” by CAOS group is licensed under a Creative Commons Attribution-Non-Commercial-No Derivative Works 3.0 Germany License.
Based on a work at spectroscopy.wordpress.com.

This is the principle explaining the mirages, gradient index lenses and fibres.  Amaze your friends by telling them that you put a black hole behind the recipient in order to create a huge gravitational field which bends light beams (General theory of relativity). A friend was convinced that we put a strong magnet below !!!

When properly poured, the sweet water will create a mixture with a gradual refraction index. The bottom will have a higher refraction index than the top. When a light beam travels inside, its direction will bend continuously (principle of Fermat)

In order to success the mixture:

1. Saturate the water with sugar. You can go faster by heating the water
2. Put FIRST the fresh water in the recipient and then the sweet water at room temperature. The saturated water will sink creating the gradient.
3. Do NOT shake or mix the solution once you pour the sweet water

Bending a laser beam by CAOS group is licensed under a Creative Commons Attribution-Non-Commercial-No Derivative Works 3.0 Germany License.
Based on a work at spectroscopy.wordpress.com.

We present our experimental results on the transmission of the 200 mm F/2.8 EF Canon objective

Transmission curve

Discussion

1. We choose this objective as a camera lens to image the echelle spectrum of our FLECHAS instrument because its excellent image quality in a very broad spectral range (400 to 700 nm). More information and reviews in these 3 links 1 2 3
2. One of our requirements is to procure optics for the spectrograph to reach the  Ca II lines (393.3 – 396.8 nm). The transmission of many objectives goes down rapidly below 400 nm. We got this Canon objective and decided to measure its transmission in the FLECHAS foreseen spectral range.
3. The transmission at 390 nm is 73 %, it is excellent for our amateur purposes. The transmission (52%) at 370 nm is still convenient for deep UV applications

Measurement procedure

List of components

• Source of white light: halogen lamp 50 W.
• Fibre bundle
• Monochromator Jobin-Yvon HII-25. 600 lines/mm @ 500 nm. f =250. F/5. Incidence-diffracted angle = 50º. Dispersion: 6.48 nm/mm
• Collimator: doublet linos 25 mm diameter with 60 mm focal length
• Objective Canon model EF 200mm, f/2.8L II USM.  Filter size 72mm. Length 138mm.
• Detector: CCD camera SBIG ST-1603ME. 1530×1020 pixels 9×9 um.
• Optical rail
• Supports for CCD camera, objective and monochromator.

Procedure

1. Connect halogen lamp to power supply. Power cooling fan. Power halogen lamp max 12v. Do not use any density yet.
2. Attach one end of the fibre bundle to lamp. The other end attached to a support mounted in a rail illuminates the entrance slit of the collimator.
3. Set the monochromator to a wavelength aprox. 600nm (yellow).
4. Wide open both entrance and output slit of the monochromator.
5. Place the doublet (collimator) to the output of the monochromator.
6. Dimm the ambient light and observe with a piece of white paper as screen where the image of the slit get focused.
7. Adjust the collimator until the monochromator light focuses at proximately 160mm from collimator.
8. Place the CCD camera in the optical rail at the focusing distance. There must be a gap space between collimator and CCD  enough to insert  the Canon objective (length 138mm). The chip is oriented parallel to table. Note that the beam is not perfectly parallel but sligthly convergent. See the discussion above.
9. Switch on the CCD, take some exposures to center the image in the CCD.
10. Insert the Canon objective between collimator and CCD with rear side towards collimator.
11. Take new exposures to confirm the image is centered in the CCD.
12. Close both input/output monochromator slits to 50 μm (Δλ = 0.6 nm passband). This is the best resolution (passband)/luminosity compromise of the monochromator.
13. Set  monochromator  wavelength to 375nm (counter = 200) and start taking exposures with and without objective. Avoid saturation and signal levels in the non-linear zone (>45000 counts).  Save the images.
14. Increase the wavelength (counter=+20) . Adjust exposure time if necessary. Use density to reduce flux to avoid exposure time smaller than one second..
15. When finishing exposures, compute ratio between  objective and direct monocromator light. Write the results in an excel table and plot the percentage versus wavelength.

Tips

• Allow some time (10min) for the halogen lamp to stabilize flux before taking exposures.
• When measuring the efficiency in the UV region, use the halogen lamp at nominal voltage of 12v.
• Avoid light polution during exposure.
• Use simple auto-dark substraction with exposures to reduce background noise.
• Cool down the CCD to reduce background noise.

Authors

Carlos Guirao and Gerardo Avila

Optical efficiency of the 200 ln/mm Newport transmission grating by CAOS group is licensed under a Creative Commons Attribution-Non-Commercial-No Derivative Works 3.0 Germany License.
Based on a work at spectroscopy.wordpress.com.

We have measured the optical efficiency (transmission vs. wavelength) of the  200lin/mm, 505nm blaze 1st order, 10 deg, 58x58x10mm transmission grating of Newport (former Richardson gratings, Ref. 54-006-630R)

 and compared the results with the manufacturer ones
(ones):

Master No.         2128, Date 8/3/71

Our results are shown in the following plot:

Measurements made with unpolarized light and perpendicular to the grating (not Littrow). Date: 17 Dec 2008

Discussion

1. Richardson measurements were done on the master grating, at Littrow and parallel beam. Our measurements were done on a replica, 10 deg out of Littrow and in a slightly convergent beam.
2. We orientated the grating according to the proposed design of an echelle spectrograph (FLECHAS). The measurement correspond as per spectrograph operation configuration. In this setup the blaze wavelength slightly shifts towards the red
3. We used a convergent beam only to simplify the optical set-up. By using a laser beam and tilting it by the convergence angle, we estimated a transmission error below 3%

List of material used for the measurements

• Source of white light: halogen lamp 50 W.
• Fibre bundle
• Monochromator Jobin-Yvon HII-25. 600 lines/mm @ 500 nm. f =250. F/5. Incidence-diffracted angle = 50º. Dispersion: 6.48 nm/mm
• Collimator: doublet linos 25 mm diameter 60 mm focal length
• Transmission grating Newport 58x58x10 mm, 200 lin/mm, blazed 10°@505nm. Ref: 54-006-630R
• Detector: CCD camera ATIK 11000 4008 x 2672 pixels 9×9 um.
• OG530 bandpass Schott filter for removal of the second order spectrum
• Optical rail
• Supporters for CCD camera, grating and fiber bundle.

Procedure

1. Connect halogen lamp to power supply. Power cooling fan. Power halogen lamp max 12v. Do not use any density yet.
2. Attach one end of the fibre bundle to lamp. The other end in a rail supported illuminates the entrance slit of the monochromator.
3. Set the monochromator to a wavelength aprox. 600nm (orange).
4. Wide open both entrance and output slit of the monochromator.
5. Place the doublet (collimator) to the output of the monochromator
6. Place the slit before the focal plane of the collimator in such a way that its image will be about 20 cm away
7. Dimm the ambient light and observe with a piece of white paper as screen where the image of the slit get focused.
8. Place the CCD camera in the optical rail at the focusing distance. There must be a gap space between collimator and CCD  enough to insert  the transmission grating. The chip is oriented parallel to table. Note that the beam is not perfectly parallel but sligthly convergent. See the discussion above.
9. Power the CCD, take some exposures to center the image in the CCD.
10. Insert the grating between collimator and CCD. The grooves orientation is not relevant provided that the CCD “sees” the first and zero orders simultaneously. We orientated the grating with the grooves horizontally, i.e. the dispersion was vertically.
11. Take new exposures to confirm order zero and first order appears in the CCD. Check that the diffracted beam reaches the CCD without vignetting and for all wavelengths!
12. Close both input/output monochromator slits to 50 μm (Δλ = 0.6 nm passband). This is the best resolution (passband)/luminosity compromise of the monochromator
13. Set  monochromator  wavelength to 800 nm. Insert the orange OG530 filter to avoid the 400 nm wavelength contamination from second order.  Start taking exposures with and without grating. Avoid saturation and signal levels in the non-linear zone (>45000 counts).  Save the images.
14. Do the same procedure for 700 nm
15. Remove the orange filter, and take exposures at 600, 550, 500, 450, 400 and 390nm. Adjust exposure time if necessary. Use density to reduce flux to avoid exposure time smaller than one second..
16. When finishing exposures, compute ratio between first order of the grating and direct monochromator light. Write the results in an excel table and plot the percentage versus wavelength.

Data reduction

• Set the monochromator to e.g. at 500nm. Take an exposure without the grating. Save it
• Load the image with a image processing system like Maxim DL.
• The left picture below (inverted contrast)  shows a sub-window including the image of the direct monochromatic light. The following picture shows the same sub-window but out of the image to measure the background.
• The actual flux is the difference between the two sub-windows. In our case we computed 3.757e7 – 4.101e6 or 3.347e7

• Introduce now the transmission grating between the monochromator and the CCD. Take an image with the same exposure time as the direct image (next 2 pictures).  In this case the CCD will image the order zero (weak spot  at the right) and  first order (strong spot at the left).
• Take sub-windows on the image of the first order as described above
• The absolute flux corresponding exclusively to the first order is computed as the image of the first order minus the background, in our case was 2.969e7 – 4.115e6 = 2.558e7

• The transmission at 500nm will be the coefficient between direct light and first order, i.e. 2.558e7 / 3.347e7 = 0.76 or 76% of the direct light goes directly to the first order.

Tips

• Allow some time (10min) for the halogen lamp to stabilize flux before taking exposures.
• When measuring the efficiency in the UV region, use the halogen lamp at nominal voltage of 12v.
• Avoid light pollution during exposure.
• Use simple auto-dark subtraction with exposures to reduce background noise.
• Cool down the CCD to -25 C to reduce dark current.

Authors

Carlos Guirao and Gerardo Avila

Optical efficiency of the 200 ln/mm Newport transmission grating by CAOS group is licensed under a Creative Commons Attribution-Non-Commercial-No Derivative Works 3.0 Germany License.
Based on a work at spectroscopy.wordpress.com.

In this post we want to show through pictures and drawings the process of assembling a bare fibre into a protective jacket and ended with commercial connectors for spectroscopy purposes. In particular, we have prepared a 10m, 50μm core fibre with SMA connectors and protected with a  square-locked stainless steel tube.

Documentation

A very descriptive document  is the instructions  sheet 408-9863 distributed by Tyco Electronics: OPTIMATE FSMA Fiber Optic Connector Types 905 and 906 in PDF format. The document describes the assembly process fot their SMA connectors types 906 and 905 for data and telecommunications applications. It  is basically the same process we use for linking telescopes to spectrographs were we take special care to reduce the focal ratio degradation.

The User Guidelines from Polymicro contain salso very useful information about the handling of fibres.

Material

• Fibre: Silica Optical Fiber  Polymicro, Step Index, Numerical Aperture 0.22, Core 50 µm, Clad 70 µm,  Buffer 90 µm. Ref. FBP050070085. Other characteristics at Polymicro Technologies. Price ~3.5 $/m
• Tube: Square-locked stainless steel tube from Kientec Systems model SLP-40N (internal diameter 4 mm) with PVC sheath. Price ~4.68$/m
• Connectors: SMA-905 connectors from Kientec Systems model 504-R-Z-127-A3-3, ferrule type: zirconia, ferrule ID 127 µm. Price ~56$/10 pieces
• Adhesive: Epoxy two components, transparent, 2 minutes  curing, from UHU profi-shop. Product UH45705. Price ~6€/35 gr

Tools

• Complete polishing kit from Thorlabs

or separated tools like:

• Sapphire-tipped Scribe Tool from AMP Netconnect or Diamond Scribe from Thorlabs
• Crimper Hand Tool from AMP Netconnect
• Polishing Bushing (Disc) with SMA from Thorlabs
• Polishing Sheets 3 µm and 0.3 µm from AMP Netconnect or Thorlabs
• Polishing Plate from Thorlabs

• Miscellanea: scissors, alcohol (propanol, isopropanol or methanol), acetone, water, microscope, optical tissue

Considerations before purchasing

• Fibre: Best optical fibres for linking telescopes to spectrographs are multimode step index fibre with high UV transmission. We advice to buy fibres protected with polyimide jacket because you can leave it into the connector making it more robust against strenghts. Always order some more fibre, e.g. 1 meter longer than required in order to operate it with some comfort.
• Connector: Check carefully both, the diameter of the fibre including the buffer/jacket and the inner diameter of the connector ferrule. Remember that the standard ferrule diameter is 125 µm, therefore you can accommodate fibres with buffer/jackets of up to 125 µm diamter, or with cladding of up t0 125 µm if the jacket is removed (see Polymicro document here on how to remove the jacket).  The rear part (boot type or tubing) has to fit in the protective tube. If the fit between connector and tube is too loose you may need to use some crimping tool.
• Jacket/Tube: the stainless steel tubing is more expensive than the plastic one but it offers the highest protection against accidents,  forced loops and light pollution.
• Abrasive sheets. After experience in polishing, we found that we need basically 2 abrasive sheets, the 3 and 0.3 μm. For rough lapping (reducing the excess of glue, for example), we use very fine sandpaper (P240 or higher, grain < 60 μm)

Assembling process

• Preparing the mettalic jacket. Use a drill machine provided with a grinding corundum weel to cut the mettalic jacket to the required length first, and to polish and round both ends second.
  

• Tubing the fibre. Fibres with polyimide jacket may be slided directly inside the metallic jacket.  We found the contact of the fibre against the metal does not break the fibre. The fibre is usually delivered rolled in a fibre wheel. Place the wheel on a rod or long screwdriver for un-wheeling.  If the fibre length is below 4 meters,  you may try to push it gently, with the hand, inside the tube. For that,  lay the tube straight on the floor. For longer fibres, you can try by vertically hanging the tube. If the high of the building is not enough, you should insert first a guide into the tube before you pass the fibre. The guide can be a steel wire used for hanging the curtains at home. In our case, we used an old fibre plastic cable with an standard 3mm diameter. It is stiff enough to pass up 20 m!  Once the guide is tubed, we glued it to the fibre end with a drop of any fast cyanoacrylate adhesive. When pulling the guide, do not pull to fast to avoid breakage. Leave at least 20 cm of fibre out of the tube.
• Manipulating the tube with the fibre inside. Once you passed the fibre and if the jacket is long (>10m), do not roll up the jacket in a wheel but fold it in halves: the tube lies straight on the floor, take a tube end bring together the tube ends. Use masking tape to hold the ends. Next, bring the first folded tube to the ends, etc. The reason is to avoid the differential length between the fibre and the tube when rolled. In this case the fibre “shrinks” with respect to the tube. After assembling connectors and straighting the cable, the fibre is “longer” and adopts a serpent shape inside the tube creating a high focal ratio degradation.
• Gluing the connector to the jacket and to the fibre. First, clean the fibre ends with acetone. Pass the connector into the fibre (Figure). Check that the rear side of the connector enters properly into the tube.

Before you prepare the glue, be sure you have all material ready, especially the tissue paper in case the glue goes in non desirable places. Prepare the glue. Remember that you have just 2 minutes to use the glue before polymerization! Put a drop of glue around the rear side of the connector and slide it into the tube.  Be sure you do not glue the nut of the connector! Do the same operation for the other fibre end. Check that the fibre ends slide free inside the ferrules, i.e. that the glue has not touch the fibre. If yes, you can still proceed but ensure that the fibre will not be longer than the tube.

The previous operation should be done inside the 2 minutes. So, at this stage do not try to glue the fibre with respect to the ferrule. It is better to prepare a new glue for this operation.

In order to glue the fibre to the ferrule, put a small drop of glue just at the ferrule end and the fibre. Take the fibre with your fingers and slide the fibre into the ferrule in and out by around 3 millimeters in order to moist with glue the inner side of the ferrule.

Immediately  after, apply fo a few seconds some heat with a hairdryer. This will increase the fluidity of the glue and you will obtain an homogenous distribution of the glue  around the fibre. When properly applied, the glue will take the shape of a rounded cone around the fibre. The glue will hard inside 5 minutes but we advice to wait at least 5 hours tobe sure that the glue is hard enough before to cleave and polish the fibre.

• Cleavage of the fibre. Once the glue is hard, you can proceed to cut the fibre (Figure).

Credit: Tyco Electronics

In order to avoid axial breakages (breakages which go along the fibre axis and go inside the connector), use a cleavage tool with a sapphire or diamond blade  as the one described in Material section. If you do not have it, you can still try with good sharped scisors, but DO NOT cut the entire fibre, just make a mark on the polyimide. To brake the fibre, take it with your fingers, slightly tilt it and pull it out from the ferrule until it breaks.

Estimate the thickness of the glue in front of the ferrule. In the case the thickness of the polymerized glue  is bigger than 1 mm, proceed to remove it, otherwise you can directly polish it as explained below. To remove the excess of glue, use a very fine sandpaper (P240 or higher, grain < 60 μm).

• Lapping. Place the sandpaper on a glass plate or a very flat surface. Moist it.

Tilt a bit the connector and gently slide the ferrule against the sandpaper along the tilt. DO NOT come back with the tilted connector to avoid internal brekage of the fibre into the ferrule. Turn the ferrule around its axis of a quarter of turn and lap again.

At this stage, you can check with a microscope objective (10 X is optimal) the state of the fibre. Check that the fibre is not broken. For that illuminate the fibre from the other end.

Repeat the lapping until the glue thickness is around 0.3 mm (~ 3 times the fibre diameter). With a water moisten paper tissue, clean thoroughly the fibre end.

• Coarse polishing. Before you polish the fibre, you have to flat the excess of glue on the ferrule

For that you can use the 3 μm  fibre abrasive paper without using the connector support. Place the abrasive paper on the glass plate and proceed to lap the fibre maintaining the ferrule perpendicular to the plate. Go on until you leave a fine layer of glue on the ferrule (around 100 µm, diameter of the fibre). Clean the fibre end with water.

Credit: Tyco Electronics

Insert the fibre connector into the SMA polishing support. Do not screw the nut until the end but leave a bit of play to start the polishing. This will avoid breaking accidentally the fibre end when the excess of glue is still thick. Take the connector and not the support and begin to polish. Follow an 8 shape movement as shown in the Figure.

Control the thickness of the glue and when it is thinner as around 50 μm (half of the diameter of the fibre), you can firmly screw the connector against the polishing tool. Check that you did not break the fibre along the axis (fissure).

Take the polishing tool with your hand and proceed to polish by doing the 8 shape movement. Control the polishing quality and check that the fibre has not been broken. You can accept chips on the edges of the fibre including the cladding but confirm that the core is totally free.

If you are not going to glue the fibre end against a lens or glass plate, you can leave a thin layer of glue, the fine polishing will be easier. If not, keep lapping until, ideally, you almost reach the ferrule. If there is still a fine layer of glue, the fibre is still out of the connector and when you pass to the fine polishing you will not be disturbed by the ferrule. If you have reached the ferrule, of course, you are not done, but you have to finish the fine polishing with some precautions.

• Fine polishing. Before you pass to the fine polishing (0.3 µm), clean thoroughly the ferrule and polishing tool.

This is important to avoid contamination of the fine abrasive pad with thick grains which can make undesirable scratches on the fibre. Dismount the connector and clean with a moisten tissue the inner wall of the tube and inside the groves of the polishing tool.

Put some drops of water on the abrasive and polish in the usual 8 shape way. Check the polishing quality with the microscope. If you notice that you have only polished the ferrule and not the fibre, it means that you went too strong with the coarse polishing and the fibre is hided inside the ferrule.

There are several possibilities:

1. You keep polishing with the fine abrasive until you reach the fibre end
2. You come back with the 3 µm polishing grain and polish smoothly to expose the fibre
3. You polish with a cloth pad and liquid cerium oxide fluid

The last method requires additional material like the oxide oxide suspension (Buehler polishing products). If you can procure it, place on the glass plate a clean, smooth and plain piece of cloth. Moisten it with water and apply some drops of oxide oxide. Polish with the normal 8 shape movement.Following pictures provide indications on the quality of the polishing.

Credit: Tyco Electronics

Example  of a 50 μm polished fibre. Click on the picture to enlarge. In this particular case, the fibre protrudes from the ferrule by about 30 μm. Note also that the polyimide jacket has a diameter of 90 μm and the ferrule 125. The decentering is extreme!

If you have foreseen to glue a mini-lens in front of the fibre or glue it against a glass plate. You do not need an extreme polishing quality. Usually the residual digs and scratches vanish when you apply the glue.

Authors

Carlos Guirao and Gerardo Avila

Assembling a fibre with SMA connectors by CAOS group is licensed under a Creative Commons Attribution-Non-Commercial-No Derivative Works 3.0 Germany License.
Based on a work at spectroscopy.wordpress.com.

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 10^o 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 15^o (not 10^o ). 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 (ø_i = nø_r).

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.

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

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:

where f is the focal distance of the lens, d_f the distance of the fibre end to the lens and d_t 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

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

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 is a very good option. These lenses normally reduce F/10 beams into F/6.3. 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).

This configuration, however, has the same problem as the one described in case d), namely, the pupil of the telescope is not at infinity with respect to the fibre end and therefore there is a slight increase of FRD. Fortunately for concrete examples like the Celestron F/6.3 reducer, the image of the pupil with respect to the fibre end is “very far away” and therefore the degradation is very small (equation F/#_v in Section 5.1.2). Indeed, in the case of a Celestron reducer, its focal distance is 231 mm. The focal plane of the telescope must be placed at around 100 mm with respect to the reducer. The image of the star will be then at around 63 mm below the lens. Finally the image of the telescope pupil will be around 200 mm below the lens. Therefore the distance of the pupil with respect to the fibre will be around 140 mm, i.e. relatively “far away”. Applying the mentioned equation in Section 5.1.2, the beam aperture at the edge of the fibre core will be F/6.28. The FRD is indeed very small.

A more annoying problem with this solution would be the limited aperture into the fibre (F/6.3). We have largely discussed in Section 4.4 the necessity to work with fast apertures into the fibre to reduce the FRD. If you decide to work at F/6, you will lose around 35 % of the flux. If you want to increase the efficiency this configuration is not appropriate when a commercial focal reduced is employed. You can still use a lens with shorter focal length to inject a beam with faster beam aperture (< F/6) but you have to carefully check the image quality of the spot to avoid flux loses into the fibre.

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 45^o 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):

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:

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

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:

Finally the total vignetting to the three contributions is:

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 15^o and illuminated by an F/5 beam, the vignetted flux will be around 36 % !

Conclusions

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

Author:

Gerardo Avila*

Contributions:

Carlos Guirao*

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

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.

The purposes of our Chapter on Optical Fibres are:

1. To enumerate the advantages and drawbacks using optical fibres to detach the spectrograph from the telescope. The astronomer has to evaluate the pros and contras to decide to use an optical fibre according to the observation purposes, instruments available (telescope and spectrograph) and budget restrictions
2. To describe the more relevant parameters of fibres like optical transmission and focal ratio degradation. These parameters should define the design of the optics to couple the fibre to both, the telescope and spectrograph
3. To recommend the most appropriate fibres for amateur spectroscopy. We revise the standard fibres used for telecommunications and advice the most appropriate fibres available on the market.
4. To provide tips and tricks to prepare and evaluate fibre links. We intent to explain the techniques to protect, polish and adapt the fibres with the cheapest components

We hope you will find useful all the information contained in these posts and enjoy doing astronomical spectroscopy!

The workshop described the complete process of integration and alignment of an Echelle spectrograph assembled on a commercial breadboard. We presented the optical design, efficiency and a preliminary data reduction as well. This data reduction included only wavelength calibration of the instrument.

The Power-Point presentation has been completed with some notes and comments  and it is now available for download (PDF format):

• Integration and alignment of FLECHAS

The workshop was also filmed -except the last half hour- and the videos are available at (heavy files!)

• CAOS workshop at ASPA Conference Bebra May 9 2010 (video 1. mpg)
• CAOS workshop at ASPA Conference Bebra May 9 2010 (video 2. mpg)

Integration and alignment of FLECHAS by CAOS group is licensed under a Creative Commons Attribution-Non-Commercial-No Derivative Works 3.0 Germany License.
Based on a work at spectroscopy.wordpress.com.

• An_Atlas_of_the_Thorium-Argon Spectrum-3900-9000 Å Region. ESO. S. D’Odorico, M. Ghigo, D. Ponz.
• CASPEC_Thorium-Argon_Atlas-3050-3650 Å Region ESO. L. Achmad, L. Pasquini

1. Coupling lenses

1.1. Purpose

As described in Characterization of optical fibres, a way to reduce the FRD is to launch the telescope beam into the fibre with the faster possible aperture (lower F/#). This can be achieved with appropriate lenses or a tapered fibre. As a general rule and following the FRD measurements taken in laboratory, a coupling lens should be used for telescope beams open between F/5 and F/8. For telescope beams slower than F/8 the use of a coupling lens is imperative! While for telescope beams faster than F/5 it is not really necessary. In terms of amateur telescopes, most Schmidt-Cassegrain or refractive models have F/10 apertures or slower. In such cases you must need to reduce the beam before the fibre in order to reduce the FRD. The Dobsonians and Newtons with apertures between F/5 and F/6 are at the limit but still can be coupled directly to the fibres. Some reflective telescopes allow using the prime focus opened to F/3 or F/4, in this case the fibres can be optimally coupled directly to these beams.

There are basically two ways to couple a telescope beam into a fibre, to project either, the image of the star directly on the fibre end or the pupil of the telescope. Both methods have their advantages and drawbacks as explained in the next two sections. Tapered fibres are discussed at the end of the post.

1.2. Image of the star on the fibre end

A positive lens of any focal distance may be used to image the star on the fibre input end. Figure 1 shows two optical layouts where the image of the star delivered by the telescope is projected on the fibre end. The distances of the telescope focal plane to the lens and from the lens to the fibre can be determined by using the well known Gauss equation. The reduction factor between the F/# of the telescope beam and the aperture of the beam transmitted along the fibre must be introduced in this equation.

Figure 1. Image of star on the fibre end with a single lens. Above: the star is a real object with respect to the lens. Below: the star is virtual

In the upper layout of Figure 1 the star is a real object with respect to the lens. Its image is on the fibre and stays after the focal plane of the lens. Since the pupil is practically at infinity, its image is at the focal plane of the lens. In the lower layout the star is “injected” through the lens and therefore it is a virtual object to the lens. Its image is placed before the focal plane and therefore before the image of the telescope pupil!

If F_t is the aperture (F/#) of the telescope, F_f the wished aperture along the fibre, f the focal length of the lens, then the distances from the lens to the star (d_t )and to the fibre (d_f ) are given by:

and

As a practical example, let’s assume that we have a single and thin lens with a focal distance of 10 mm and a telescope delivering a beam open to F/10. If we want to reduce the beam to for example F/4 into the fibre, we will have:

f = 10 mm, Ft = 10 and Ff = 4,

therefore the distances from the lens to the fibre and to the star (telescope focal plane) are

df = 14 mm and dt = 35 mm respectively

However, the reduction of the telescope aperture into the fibre applies only for a point on the optical axis. Some beams coming from any other point of the star (drawn in red) will enter into the fibre with higher apertures (F/#). Theoretically, only the beam from the axis would reach the spectrograph collimator without vignetting. Other beams along the field will be gradually vignetted. This vignetting depends basically of the focal length of the coupling lens. This issue is explained by the fact that the pupils of the telescope and the fibre are not properly matched. Indeed, the image of the telescope pupil is usually far away from the lens (focal distance of the telescope) and therefore its image will be close to the focal plane of the lens. On the other hand, the pupil of an optical fibre is at infinity (Characterization of optical fibres), so, smaller the focal length of the lens, closer the telescope pupil will be to the fibre and thus higher will be the vignetting for points out the centre.

The red beams in Figure 1 define an F/#_v according to the following equation:

Where f is the focal length of the coupling lens, φf the diameter of the fibre, F/#T the telescope aperture and F/#f the wished beam aperture in the fibre.

As an example, if you want to reduce an F/10 telescope beam into an F/5 in a 50 µm fibre with a f = 5 mm coupling lens, the actual red beam in the fibre will degrade to F/4.5. However, if you use a lens with a longer focal length, for instance 100 mm, as in the bottom layout in Figure 16, the red beam will degrade only to F/4.8. In other words the vignetting will be significantly reduced.

Another way to overcome the incompatibility between the pupils is simply to enlarge the collimator aperture to accept all the beams. The price to pay is to enlarge all the optical components of the spectrograph accordingly! Still another way is to keep constant the collimator diameter but reducing the focal distance of the collimator in order to increase its F/#. The price to pay in this case is to reduce the resolving power of the spectrograph (next Post)

The ideal solution to this dilemma is to inject the telescope beam with an optical system which keeps the telescope pupil at infinity. In the optics jargon, this system is called telecentric. Figure 2 shows an example with 2 single lenses.

Figure 2. Optimal coupling between the telescope and the fibre when the star is imaged on the fibre end.

The image of the star (telescope focal plane) is placed at the focal plane of the first lens. The image of the star is sent to infinity and the image of the telescope pupil will fall on the focal plane image of the first lens. The second lens focuses the image of the star on the input fibre that corresponds to the focal plane image of the second lens. The second lens is placed in such a way that its object focal plane coincides with the image focal plane of the first lens. In this case, the second lens will send the image of the pupil to infinity. Under this configuration all rays issued from each point of the star will enter into the fibre with the same aperture (F/#). By the way, the ratio of telescope aperture and the beam aperture inside the fibre is given by the ratio of the focal distances between the lenses:

We notice that any couple of lenses with the appropriate focal distances ratio may be used. However, it is preferable to use lenses with small focal distances to have a compact design. Usually they are few millimetres only. The second lens may be designed in such a way that the rear surface of the lens is in contact with the fibre. In this case, two air-glass surfaces are eliminated and the optical efficiency is therefore increased.

The next step is to select the most appropriate coupling lenses. As amateurs, we look for the best performance-to-price ratio. By performance we meant both, the best mage quality and the highest optical transmission. Among the single lenses we can buy on the market (Linos, Edmund Optics, Thorlabs, etc.) there are the plano-convex, bi-convex, 6:1 radius ratio lens (convex lens where the radius of one surface is 6 times the radius of the other surface), gradient index rod lenses and doublets.

In the case to use a single lens and without going into much detail, the best choice (but the most expensive) are the doublets; they reduce spherical and chormatic aberrations. Next in the list are the bi-convex lenses. In both cases, the image quality increases with small focal lengths, but unfortunately the vignetting increases due to the pupil incompatibility. As for the aberrations only, there is a big difference between a doublet and a bi-convex lens. Optical design simulations show that when using a 5 mm focal length doublet to reduce an F/10 beam into a F/5 on a 50 µm fibre, only 4 % of the flux is lost for a star matching the fibre diameter. For a bi-convex lens the losses increases to 27 % ! (Zemax calculations)

As for the two lenses configuration, two doublets provide an excellent coupling efficiency. Figure 3 shows the layout of the two lenses for the fibre link for the HARPS spectrograph (Performances of HARPS and FEROS fibers in La Silla ESO Observatory, Proc. of SPIE Vol. 5492 pp 669-676, Glasgow, 2004). Note that the second doublet was extended in order to glue its surface to the fibre input end. Two air-glass surfaces are then eliminated. The F/8 telescope beam was reduced to F/4 in the fibre.

Figure 3. Optical layout for the coupling between the telescope and the HARPS fibre. The star is directly imaged on the fibre end with a couple of doublets, the pupil is at infinity

Still another compact, efficient coupling system is made with two gradient index 0.25 pitch rod lenses. For a good and detailed description of these GRIN lenses consult the Melles Griot Catalog at this site: (http://www.mellesgriot.com/pdf/0015.16-15.20.pdf). Figure 4 shows the optical layout with the two lenses glued together to the fibre input end. Each lens is cut to a 0.25 pitch but different focal distances. They can be used as collimators. When the image of the star is projected on the surface of the firs lens, its image will go to infinity. On the other hand the image of the telescope pupil will be located on the output surface of the lens. The second gradient index lens acting as a focusing lens brings the image of the star on the fibre and the pupil to infinity. As in the case of individual lenses, the ratio of focal distances equals the ratio of apertures between the telescope and the fibre (equation above).

Figure 4. Two 0.25 pitch gradient-index lenses glued together to re-image the star on the fibre input end.

Usually the gradient-index lenses are delivered with a single layer of MgF2 as anti-reflection coating. Since the lenses and fibre are glued together, the optical layout shows only one air-glass surface. This configuration is therefore highly efficient as for reflectivity losses. However they show some chromatic aberrations which reduce substantially the coupling efficiency to the fibre. For example, if a telescope delivers an F/10 beam with a star of 141 µm on the surface of a grin lens of 2.71 mm focal distance and the star is imaged on a 50 µm fibre by means of a second grin lens of 0.95 mm focal distance, the flux entering into the fibre will be 90% (Zemax calculation). Another drawback of this configuration is the difficulty to align and glue properly the two lenses and to the fibre, especially when the grin lenses have different diameters.

1.3. Image of the telescope pupil on the fibre end

An alternative to project the star on the input fibre end is to project the pupil of the telescope instead. The big advantage is that only a single lens can be used, and when using plan-convex or gradient index lenses they can be manufactured in such a way that its focal plane image lies on the back surface of the lens. The fibre can be directly glued eliminating two air-glass surfaces. The front surface of the lens can be coated minimizing the reflection losses. However, there are two big drawbacks: a) the focal length of the lens depends on the fibre diameter and usually is less than 1 mm, so they are very small lenses. b) this method is only useful for telescopes larger than 1 m. For smaller telescopes, the beam to be propagated along the fibre is not properly reduced (F/# < F/5, see Characterization of optical fibres)

Before going into details, let’s describe the locations of pupils in an optical system. There are four terms to be defined: the stop, the input, the intermediate and the exit pupils. Generally speaking, the light passing through an optical system is limited by a real aperture called the “stop”. The entrance pupil is the image of the stop for an observer located in the object space (Figure 5). The exit pupil is the image of the stop but as seen from the image space. The intermediate pupils in systems with several optical elements are the intermediate images of the stop by these elements.

Figure 5. Stops and pupils in optical systems. a) The stop is defined by the lens. b) The stop is in the object space. c) The stop is placed on the focal plane of the lens. d) The stop is in the image space

When a single lens is used to image an object on a screen or detector, the stop is defined by the edge of the lens (Figure 5 a)). The lens itself limits the amount of light reaching the plane of the image, the input and exit pupils lie also on the stop plane. If a screen containing an aperture with a diameter smaller than the lens is placed in front of the lens, as in Figure 5 b), this aperture now limits the light beams. In this case the stop is defined by the aperture on the screen. For an observer placed in the object side, the image of the stop is the stop itself. The exit pupil is the image of the stop through the lens for an observer placed in the image space. In this case, the exit pupil is a virtual image.

In Figure c) the stop lies on the focal plane of the object. The entrance pupil is again defined by the stop but the exit pupil is at infinity. Finally when the stop is placed in the image space of the lens, the exit pupil is the stop itself but the entrance pupil is the image of the stop as seen from the object space. It is also a virtual image. Resuming: the entrance pupil is the image of the stop from the object space of the optical system and the exit pupil is image of the stop from the image space. Note that he stop may be defined by an intermediate lens. In elaborated optical systems, the images of the stop by the lenses or mirrors are intermediate pupils and they may be real or virtual

Most of refractive telescopes and binoculars are made by single doublets. The entrance lens defines the stop, the input and exit pupils. When you put an eyepiece at the focal plane of the telescope, the exit pupil lies very close to the focal plane of the eyepiece (the focal distance of the telescope is much bigger than the focal distance of the eyepiece). It is at this location where you must place your eye, or more exactly your pupil. It is interesting to note that the image of your eye will be indeed at the entrance lens of your telescope (Figure 6).

Figure 6. An observer must place her/his eye on the exit pupil of the binocular, therefore its image is indeed on the entrance pupil!

In Newtonian telescopes the stop is defined by the main parabolic mirror. In most Schmidt Cassegrain telescopes, the stop and also the entrance pupil is defined either by the support of the Schmidt plate or by the primary mirror. In any case the exit pupil is the image of these apertures and lie behind the M2 mirror. In all cases, the exit pupil is far away from the focal plane of the telescope. When you place an eye-piece to explore the sky images, the exit pupil is transported very close to the focal plane image of the eye-piece.

Now, coming back to the injection of the telescope beam into the optical fibre, when you put a small lens just after the focal plane of the telescope, the image of the telescope stop or the exit pupil falls almost on the focal plane image of the lens, see Figure 7. It is at this location where you must place the input fibre end. In addition, the image of the star should be placed on the focal plane object of the lens. At this location, all rays emerging from any point of the star will enter parallel into the fibre. The aperture of the beam propagated along the fibre will be defined by the size of the star. If the star is placed on other locations along the optical axis, the beams will not enter parallel and will increase the beam aperture (F/#).

Figure 7. Coupling a telescope to a fibre by projecting the pupil on the fibre input end. The telescope pupil is on the image plane of the lens and the star is on the object focal plane of the lens

If s is the size of the star (seeing), F/#tel the beam aperture of the telescope and Φ the diameter of the fibre, the focal length of the lens (f) and the aperture of the beam in the fibre (F/#fibre) are given respectively by:

As a practical example, if you have a 1m telescope opened to F/10 and a 50 μm fibre, you will need a mini-lens with a focal distance of only 0.5 mm. If you want to have an aperture on the sky of say 2.5 arcsec, the size of this aperture at the focal plane of the telescope will have around 125 μm* . The beam to be propagated along the fibre will have therefore an aperture of F/4. As we discussed in Characterization of optical fibres, this aperture is at the limit in terms of FRD. In order to reduce the FRD, the beam has to be faster (<F/4), therefore the aperture on the sky or the telescope focal distance should be higher.

2. Tapered optical fibres

As mentioned in Section 3.1.4. tapers may be used to couple telescopes to spectrographs. They may replace the troublesome micro-lenses to reduce the FRD. The taper may be directly placed at the input fibre end to catch the flux of a large portion of the star and the output end to the spectrograph. It looks a very convenient device where most of the flux of the star enters into the fibre. It also increase the resolving power of the spectrograph because the equivalent “slit width” is smaller. However, there are a number of problems:

1. The beam aperture of the output beam increases with the ratio of the diameters between the input and output fibre ends
2. The taper must be linear and long, otherwise the FRD increases very fast
3. Commercial tapers are very expensive (for amateur purposes)
4. The measured efficiency is low than expected and therefore not interesting

If the taper is long enough (L >> core diameter, in practice longer than 10 cm), the output aperture (F/#out) is given by:

where F/#in is the input beam aperture, Φin the diameter of the taper receiving the flux and Φout the output diameter. For example, if you want to reduce your fibre from 100 µm to 25 µm and your telescope provides an F/10 beam, the output beam will be F/4. A taper with a 25 μm fibre is very interesting for amateur purposes but it is difficult to manufacture and therefore very expensive!

At ESO we have tested 4 tapers from different manufacturers. Two of them provided throughputs comparable to the ones of fibres coupled with lenses and the other two with much lower efficiencies. The Table below summarize the results.

As you can deduce from the results, the throughputs are not better than the solution with lenses. In conclusion, we do not advice to use tapers for coupling telescopes to spectrographs.

* If f is the focal distance of the telescope (f = Φ•F/#), one arcsec projected on the focal plane of the telescope, or plate scale will be s = 4.85•f, where the focal distance of the telescope is expressed in meters and s will be given in μm/arcsec. One arcsec = 4.85 E-6 radians. A very good approximation is to say that the plate scale (in μm/arcsec) is 5 times the focal distance of the telescope (in meters).

Author:

G. Avila*

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

Linking a telescope to a spectrograph through an optical fibre. Part I 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.