# Inexpensive image slicer with mirrors

Paper submitted to Experimental Astronomy A Bowen-Walraven image slicer with mirrors G. Avila* , C. Guirao* *European Southern Observatory, Karl-Schwarzschild-Str. 2, 85748 Munich, Germany

Abstract

This paper describes a prototype of a modified Bowen-Walraven image slicer with mirrors. The measurements of the optical efficiency and slit edges quality are also reported.

Keywords: image slicers, optical fibres, Bowen-Walraven

1. Introduction

Bowen-Walraven image slicers (BWIS) have been used in a wide number of spectrographs like CES [1], FEROS [2], UVES [3], CFT [4]. They use a thin glass plate where the light is transmitted along by total internal reflection. A base prism is glued to the plate to “cut” the internal reflection of the transmitted beam. By choosing an appropriate configuration, the slices are arranged on a line simulating the slit of the spectrograph. This device is complicated of manufacturing and therefore expensive.

We propose an image slice based on the same principle of the clasic BWIS, i.e. with successive reflections but using mirrors instead of a glass plate working by total internal reflection. This new design can be manufactured with two simple inexpensive mirrors making it affordable for amateur spectroscopists.

In Section 2 we describe the principle of the traditional Bowen-Walraven Image Slicer, its performances and limitations. In Section 3 we show the same model but with mirrors. In Section 4 we present a prototype foreseen for PUCHEROS spectrograph and we will discuss its performances and limitations.

2. The Bowen-Walraven IMage Slicer

Figure 1 displays the optical layout of the Bowen-Walraven Image Slicer (BWIS) showing the slicing principle. One of the edges of a thin glass plate is cut at 45° and polished. This face will be the input window of the image slicer. For clarification purposes let’s assume that a cylindrical light beam is launched to this window. This beam will be transmitted all along the plate by total internal reflection (Figure 1 b). Looking from the incoming beam, the beam is successively reflected by the plate. Figure 1 c shows the footprint of the successive reflections. The efficiency of the beam is only limited by the internal absorption of the glass. The plate is usually made in silica, therefore the absorption is almost null.

Figure. 1. The typical Bowen-Walraven image slicer. From left (Figure 1 a) : 3D view showing the plate, base prism and incoming beam . Internal transmission in the parallel plate. Top view: footprint of the incoming beam along the plate. Plate and prism showing the slices. This configuration is for 3 slices.

A so-called base prism is glued to the plate by molecular contact. This prism is basically an equilateral 45° prism but one of its lateral faces is inclined with an appropriate angle (Figure 1 d). The input beam light is sent in such a way that the light spot touches the edge of the base prism. This portion of the spot is not reflected but transmitted through the prism. This small beam eventually leaves the image slicer and it is sent to the collimator of the spectrograph. The rest of the beam is reflected two times more by the plate. Another portion of the beam touches the edge of the prism and it is transmitted to the prism. This process is repeated until all the input beam is sliced by the edge of the base prism. Al the emerging slices are arranged on a line forming the slit of the spectrograph. The slicing edge of the base prism must be very sharp to properly define the edges of the slit.

The BWIS shows two important advantages:

1. High efficiency. Throughputs more than 90% have been reported [??].
2. A big spot may be sliced several times. The resolving power of a spectrograph may be substantially increased with a high throughput. The image slicer used at the 3.6 m telescope in La Silla where a fibre links the CES high resolution spectrograph, slices 7 times the image of the fibre.

Unfortunately there are a number of disadvantages limiting its scope of applicability:

1. The equivalent slit is inclined along the optical axis of the spectrograph collimator (Figure 1 e). The image of the slit projected on the detector has a ‘corset’ shape: it is sharp at the middle of the slit and progressively defocused towards the edges. This problem reduces slightly the resolving power of the spectrograph. This problem may be reduced by re-shaping the exit face of the base prism, but this increases the complexity of the device making the manufacturing process more expensive.
2. The glasses usually are silica to ensure high throughput. However the refraction index of the silica is relatively low and therefore the critical internal reflection angle limits the aperture beam to around F/11 or slower.
3. The BWIS is a expensive device. The plate must be very thin, especially for small spots to be sliced and the base prism carefully cut and polished. The edge of the slicing face must be very sharp to ensure a good quality of the edges of the slit. In addition, the pieces must be glued by molecular contact, which is not a standard technique for all optical manufacturers.

3. The Mirrors Image Slicer

With the same principle, the silica plate in the traditional BWIS could be replaced by two parallel mirrors in order to generate the successive reflections. The edges of the mirrors are placed in such a way that a portion of the beam is not anymore reflected but leaving the arrangement towards the spectrograph. Figure 2 shows the optical layout.

Like in the glass plate, Figure c shows a top view (incoming light beam) showing the footprint of the beam along the successive reflections inside the mirrors. The mirror-2 which is below mirror-1 is twisted by an appropriate angle (60° from the top view, 67.8° on the plane of the mirrors) to get two slices. For three slices, the projected angle between the mirrors (edges) has to be 70.53°.

The light spot is then placed in the corner between the two mirrors. It touches the edge of mirror-1 and half the spot surface is cut by mirror-2. Under this condition, half of the beam is transmitted directly to the spectrograph and the other half is reflected by mirror-2. Since the edge of this mirror is inclined with respect to the direction of the successive footprints of the input beam, the second half of the beam will leave without anymore reflections.

Since the reflectivity R of the mirrors is not 100% the second slice will have an efficiency of R2 and therefore the total efficiency will be 50(1+ R2). A not so fresh good aluminium coating will have a reflectivity of around 92% in the visible range (R=0.92), therefore the throughput for a 2 slices device will be close to 92%.

In a general case, when n is the number of slices, the throughput (E in %) of this image slicer will be:

$E = \frac{{100}}{n}\left( {\sum\limits_{i = 1}^n {R^{2(i - 1)} } } \right)$ ,

where  0< R < 1

Figure 2. The two mirrors image slicer

If an image slicer is configured to have 3 slices, its efficiency will be 85.4%. We can see that the total efficiency decreases rapidly with the number of slices. Therefore this image slicer is optimal for a two slices configuration. The traditional BWIS has a better efficiency because the losses along the glass plate are almost 0%. Theoretically it is limited by the reflection losses at the input and output surfaces of the plate and base prism respectively.

The separation of the mirrors (like in the BWIS’ plate) defines the diameter of the spot to be sliced. If s is the separation of the mirrors inclined at 45° with respect to the optical axis, the diameter of the spot d will be\$latex

$d = \sqrt 2 s$

There is, a priori, no reason not to couple the image slicers directly to the telescope, however in all known cases they are linked through optical fibres. The purpose of an image slicer is to increase the resolving power of high resolution spectrographs, therefore such instruments are usually heavy and cumbersome. An optical fibre allows detaching the spectrograph from the telescope and consequently the instrument can be placed in an isolated environment increasing the stability and precision of spectra. In practical examples like FEROS and CES instruments, the fibre output end was imaged on the entrance window of the BWIS providing an spot of 1 or 2 mm diameter. The glass plate was of around 0.7 to 1.4 mm thickness. In cases where the telescopes are much smaller and the fibre is on the order of 50 µm, the spot projected is in the order of 100 to 200 µm. In this case the thickness is 10 times smaller 70 to 140 µm ! It would be very difficult to make such glass plates. However, the image slicer with mirrors may overcome this difficulty. The separation between the mirrors could be made quite small.

4. The Prototype

We have built for the PUCHEROS spectrograph [?] an image slicer prototype with only two slices. We used a 50 µm core diameter fibre working at F/5 and a small doublet to project the fibre output end on the image slicer with a spot of 200 µm (F/20 output beam).

Figure 3. A two mirrors image slicer prototype

We made the mirrors with aluminized microscope cover glass. The edges are intrinsically well defined and they do not need to be re-sharpened. The separation between the mirrors was achieved by gluing a third cover glass in between. Usually the thickness of these plates range between 140 and 160 µm. So very close to the required thickness (141.4 µm).

This prototype provides a slit of 103 µm (check log-book)

The roughness of the slit edges were estimated to less than 5 µm peak to valley.

From Figure 3 c) we clearly see the intensity difference between the transmitted and reflected slices. The measured total efficiency of the prototype is 85% (check log-book!?). We did realize that the aluminium deposition of the cover glasses was not optimal.

After evaluation of this prototype we deduce the following advantages:

1. This model is simple, compact and inexpensive (relative to the traditional BWIS)
2. The mirrors may be approached to a point to provide narrow slits. We believe that we can still reduce the width in a future prototype down to 50 µm. If so, it would be very attractive for amateur spectroscopy applications.
3. Good enough slit edges quality

However, there is also two non negligible drawbacks:

1. The slit inclination along the optical axis is even higher than the case in the BWIS. The defocusing is given by $\Delta = d/\sqrt 2$
2. In our case the defocus between the 2 slices is 141 µm. For our slices of 100 µm width, the equivalent slit is increased by 3.5 µm {141/(2xF/20)}. This error causes a reduction of the resolving power of the spectrograph by 3.5%
3. The throughput decreases fast with the number of slices. This concept is useful for 2, maybe 3 slices with a good aluminium coating.

Conclusion

We presented in this article a prototype of a Bowen-Walraven Image Slicer made with mirrors. The advantages and drawbacks were analysed. Best performances are achieved for an image slicer with only 2 slices. Our prototype provides a slit of 103 µm with a total efficiency of 85%.

This concept may be a good alternative to increase efficiently the resolving power of small spectrographs linked with optical fibres.

Acknowledgments

We want to thank the workshop of the Max-Planck-Institut für Extraterrestrische Physik through Vadim Burwitz and Richard Mayr (Ausbildungsleiter)  for their support to build the prototype.  J. Rodriguez for corrections and comments to the manuscript.

References

[1]    CES [2]    FEROS [3]    UVES [4]    CFT

Inexpensive Image Slicer with Mirrors 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.