Focal Ratio Degradation: A new perspective

Transcription

1 Focal Ratio Degradation: A new perspective Dionne M. Haynes* ab, Michael J. Withford a, Judith M. Dawes a, Roger Haynes b, Joss Bland-Hawthorn c a Centre for Ultrahigh bandwidth Devices for Optical Systems (CUDOS), MQ Photonics Research Centre, Macquarie University, Sydney, Australia. b Anglo-Australian Observatory, Sydney, Australia. c School of Physics, University of Sydney, NSW, Australia. ABSTRACT We have developed an alternative FRD empirical model for the parallel laser beam technique which can accommodate contributions from both scattering and modal diffusion. It is consistent with scattering inducing a Lorentzian contribution and modal diffusion inducing a Gaussian contribution. The convolution of these two functions produces a Voigt function which is shown to better simulate the observed behavior of the FRD distribution and provides a greatly improved fit over the standard Gaussian fitting approach. The Voigt model can also be used to quantify the amount of energy displaced by FRD, therefore allowing astronomical instrument scientists to identify, quantify and potentially minimize the various sources of FRD, and optimise the fiber and instrument performance. Keywords: Optical fiber, focal ratio degradation, FRD, scattering, surface roughness, astronomical instrumentation. 1. INTRODUCTION Multimode optical fibers have been used as light pipes in astronomical instrumentation for the past 30 years because of their unique ability to take light from the focal plane and spatially reformat it at an image plane. This has revolutionized spectroscopy by enabling remotely mounted highly stable multi-object spectrographs. As with all optical components optic fibers are not perfect and light loss can occur. One major manifestation of light loss in systems employing multimode optical fibers is Focal Ratio Degradation (FRD). In a perfect fiber the light would emerge at the same f-ratio as it entered, however due to minor imperfections in the fibers the emergent light is more spread out in angle (faster f- ratio) than the input beam [1], hence the phrase focal ratio degradation. This beam spreading can result in a loss either in throughput or resolution in astronomical spectroscopic applications [2]. In order to reduce the possible light losses in multimode fiber based systems, instrument designers need to quantify FRD and minimize its impact prior to designing the instrument components such as the spectrograph collimator. FRD measurements on fibers are nothing new and have been occurring since the first multifiber systems were used in astronomy over 30 years ago [3], [4], however there have been some inconsistencies in the results reported by different researchers even for fibers from the same manufacturer and the same type. Much of this has been attributed to varying measurement techniques and fiber end preparation techniques. There are three main components that can contribute to FRD; mode coupling, scattering and diffraction, and these can be influenced by six factors; material irregularities, fiber geometry irregularities, macro bending, micro bending, end-face surface roughness and fiber geometry. Some of the contributors to FRD can be very sensitive to the external environment and are likely responsible for the inconsistent results reported by researchers. Two FRD measurement techniques commonly used are the cone [5], [6], [7], [8], [9], [10] and the parallel laser beam [2], [11], [12]. The cone technique gives a good estimate of the total light loss that might be expected in a fiber based system, however it can be highly sensitive to alignment errors and does not provide information about the possible sources that may be contributing to any FRD. The parallel laser beam technique is highly sensitive to small changes in FRD and is commonly used as a quick look technique however to quantify FRD it assumes that the radial profile of the FRD distribution is a Gaussian and measures FRD in terms of the FWHM [2],[11],[12]. This method works well when measuring the modal Advanced Optical and Mechanical Technologies in Telescopes and Instrumentation, edited by Eli Atad-Ettedgui, Dietrich Lemke, Proc. of SPIE Vol. 7018, 70182U, (2008) X/08/$18 doi: / SPIE Digital Library -- Subscriber Archive Copy Proc. of SPIE Vol U-1

2 diffusion component of FRD because Gloge s model [13] shows modal diffusion to be represented as a Gaussian profile, however if scattering is present the FRD distribution deviates away from a Gaussian profile. In this manuscript we expand on the parallel laser beam technique and methodology and present a Voigt FRD model that simulates an FRD distribution in the presence of both modal diffusion and scattering. We show how this model can be used as a diagnostic tool to identify, quantify and potentially minimize sources of FRD and improve the fiber and instrument performance. 2. EXPERIMENTAL DETAILS We investigate the impact that scattering has on FRD by changing the end-face surface roughness (δ i ) at the input end of the fiber. A sample of fibers were polished at the input end to varying degrees of surface roughness using conventional hand polishing techniques and different grades of lapping film as described below. The output face was cleaved to avoid mounting stress that is sometimes associated with mounting fibers in ferrules for polishing. The cleaved output gave an end-face surface roughness δ o ~25 nm rms. A series of FRD measurements was taken using the parallel laser beam technique [11], [12] in which a collimated HeNe laser beam is injected into the fiber at various input angles θ i, the fiber output is projected onto a screen which is re-imaged onto the ST-7 CCD as shown in Figure 1. Fiber end-face surface roughness measurements were made using a WYKO NT3300 Optical Surface Profiler in Vertical Scanning- Interferometry (VSI) mode and an Olympus optical microscope in phase contrast mode was used to inspect and image the fiber end-faces. 2.1 Experimental setup Fibre Figure 1. Diagram of the optical apparatus used to image the fiber far field light distribution (FRD distribution). This setup is referred to as the parallel laser beam technique [11] 2.2 Fiber details Fiber type: FBP made by Polymicro Technologies. Its characteristics are as follows: Low loss Broad Spectrum Fiber nm, Multimode step index, Numerical Aperture: 0.22±0.02, Silica core, Doped Silica Clad, Core diameter 140µm, Clad thickness14µm, polyimide buffer 14µm thick. This is the same fiber that is used in the AAOmega instrument on the Anglo-Australian Telescope. Proc. of SPIE Vol U-2

3 2.3 Fiber preparation For ease of handling and polishing the optical fiber ends were mounted in rigid stainless steel ferules with polyimide strain relief tubes using the low shrinkage adhesive Araldite Super strength [8],[10]. The adhesive was allowed to cure for 30 hours before polishing. Fiber samples A and B were polished by hand using wet polishing techniques, starting by roughing off with 600-grit emery paper, then 12µm lapping film, 3µm lapping film, 1µm lapping film and finally 0.3µm lapping film. The fiber end-face surface after the 12µm and the final 0.3µm stages (respectively) are shown in Figure 2 and Figure 3. Great care was taken to thoroughly clean the fiber end between each of the polishing steps to prevent polishing grit from building up in gaps in the adhesive as this can dislodge during the next polishing step and scratch the face of the fiber. The cleaning process consisted of a) suspending the fiber tip in an ultrasonic bath of distilled water to dislodge any build up of grit b) cleaning the fiber tip with isopropanol and a cotton bud, c) inspecting the fiber end-face with an optical microscope. rr -,1 Figure 2 Fiber end-face optical microscope images, (left) δ i = 270nm rms, (right) δ i = 8nm rms, taken with Olympus microscope in phase contrast mode and x100 objective. Figure 3 Fiber end-face 3D Optical Profilometer images, (left) δ i = 270nm rms section area 33 x 40 µm, (right) δ i = 8nm rms section area 88 x 114 µm, taken with WYKO NT3300 in VSI mode. 2.4 Data extraction The software package CCDOPS was used as the interface between the computer and ST-7 CCD. The software was setup to automatically subtract a dark frame from the image frame in order to remove hot pixels. The resultant image frame was saved in FITS format (see Figure 4). The Fits images were reduced using a program written specifically to analyze the FRD distribution of a multimode fiber. The program produces a radial profile of the data by first determining the centre of the annulus and then integrating the light falling within annuli of varying radii, starting at a radius of 2 pixels and incrementing by 1 pixel out to the edge of the frame. The resulting data file contains the radius in pixels, mean radial counts, total counts for each radii, number of pixels in each radii and the standard deviation of counts for each radii. The Proc. of SPIE Vol U-3

4 integration is necessary in order to smooth out the interference patterns (laser speckle) observed in the far field light distribution due to the extremely coherent laser source. The radial profile data was imported into the mathematical software package Mathematica 6 to plot the profiles and perform the data fitting (see Figure 7 and Figure 8). 3. RESULTS Figure 4 FITS images of the FRD distribution for fiber sample A with end-face surface roughness of 245nm rms (left) and 8nm rms (right). θ i = 8, δ o = 25nm rms, λ= 633 nm. Figure 4 shows the CCD image of the FRD annulus after hot pixel removal and conversion to FITS file format. The image on the left hand side is the FRD distribution of fiber sample A after preparation with the 12µm lapping film. This was measured to have an input end-face surface roughness of 245nm rms (Figure 3, left). An annulus can be clearly seen, however there is a significant amount of light scattered into the central zone and periphery. The image on the right hand side is the FRD distribution of fibre sample A after final preparation with the 0.3µm lapping film. It was measured to have an input end-face surface roughness of 8nm rms (Figure 3, right). It shows a well defined annulus with significantly less light scattered into the central zone and the periphery than for the previous image ISO Figure 5 FRD radial profile plots for δ i = 245nm rms (left) and δ i = 8nm rms (right). θ i = 8, δ o = 25nm rms, λ= 633nm. Figure 5 shows the FRD radial profiles that were extracted from the images in Figure 4. The radial profile for the 245nm rms surface (Figure 5, left) shows a large amount of the energy in the wings. When the surface roughness was improved to 8nm rms the shape of the radial profile (Figure 5, right) changed significantly showing the majority of the energy to be Proc. of SPIE Vol U-4

5 located in the central peak. The plots re-affirm the observations made with regards to images in Figure 4, i.e. that there is more light scattered away from the annulus for the higher surface roughness image (left) and less for the lower surface roughness image (right). In preparation for data fitting we truncated all data sets at the fiber numerical aperture (NA) plus tolerance ( = 13.9 ) which equated to pixel 217 in our data sets. The reason for doing this is because the light is no longer fully confined to the core and starts to be lost through the cladding once the NA of the fiber is exceeded. However, the data shows there is still energy beyond the NA (see Figure 5) possibly from two sources; the NA cut-off is not a sharp transition so some light can still propagate at these high angles; and scattering from the cleaved output end of the fiber. To check if scattering from the cleaved end was contributing we immersed the cleaved end in index matching gel (to take out the effects of end-face surface roughness) and re-measured the FRD distribution. Figure 6 shows the results. boo Output end cleaved Output end immersed IOU - So IOU ISO Figure 6 FRD radial profile plots for fiber sample B, with and without cleaved output end immersion. θ i = 8, δ i = 7nm rms, δ o = 25nm rms, λ=633nm. The FRD radial profile for the immersed output end seen in Figure 6 clearly shows an overall reduction in energy displaced into the wings of the profile. There is also a noticeable difference between the two FRD profiles beyond the numerical aperture of the fiber (pixel 217). This confirms that the cleaved output end is contributing to the energy observed beyond the numerical aperture. A standard Gaussian function was fitted to the truncated FRD radial profile data [2], [11], [12]. The Gaussian was a good fit to the central peak of the 8nm rms data, however it provided a poor fit to the energy in the wings of the profile (see Figure 7). This problem became more evident when fitting the 245nm rms data which has a large portion of its energy in the wings. We found a Lorentzian function to be a good fit to the wings of the truncated FRD radial profile data for each end-face surface roughness ranging from 245nm rms (roughest) to 8nm rms (smoothest), indicating that scattering induces a Lorentzian profile. To obtain a good fit across the entire FRD radial profile we used a Voigt function, which is a convolution of a Gaussian and Lorentzian (see Figure 7 and Figure 8) Proc. of SPIE Vol U-5

6 Voigt fit Gaussian fit A Data 50 IOU Figure 7 Comparison of a Voigt fit and a Gaussian fit for fibre sample A with an end-face surface roughness of 8 nm rms. δ o = 25nm rms, λ=633 nm. Figure 7 shows a Gaussian and Voigt fit for the 8nm rms FRD radial profile data. The Gaussian can effectively fit the central peak, however it can not map the light displaced into wings of the FRD profile. By comparison the Voigt is a good fit both in the central peak and the wings. ISO ISO r Data Data IOU 70 Voigt fit Voigt fit SO 30 IS 10 SO IOU ISO 50 IOU Rdj] ISO Figure 8 Voigt fits to the FRD radial profiles of fiber sample A, with an end-face surface roughness 245nm rms (left) and 8nm rms (right). θ i = 8, δ o = 25nm rms, λ= 633 nm. Figure 8 shows Voigt fits to the FRD radial profiles of the 245nm rms data and the 8nm rms data. These fits demonstrate that a Voigt function can model the FRD distribution of a fiber for various amounts of scatter induced by changing the fiber end-face surface roughness. Proc. of SPIE Vol U-6

7 4. DISCUSSION The asymmetry seen in the FRD radial profiles (Figure 5, Figure 6, Figure 7 and Figure 8) is consistent with the same amount of light being scattered into the central zone of the annulus as is scattered outside the annulus, however because the light is scattered into a physically smaller area inside the annulus a higher intensity is observed (Figure 4), i.e. it is due to an area effect, caused by the 2π integration and not due to asymmetry in the scattering process. We found that a Gaussian model does not accurately describe an FRD distribution in the presence of scattering as it fails to fit the wings of an FRD radial profile (see Figure 7) this is because scattering induces a Lorentzian profile. However, according to Gloge s model [13] a Gaussian function accurately describes modal diffusion, which is a major component of the FRD distribution. Therefore a convolution of a Gaussian and a Lorenztian, which is defined as a Voigt function is a more accurate description of an FRD distribution in the presence of both modal diffusion and scattering respectively (see Figure 7 and Figure 8). Because the Voigt function is modeling the physical processes happening within the fiber it can be used to quantify the contributions from modal diffusion (Gaussian) and scattering (Lorentzian) via deconvolution. By deconvolving the Voigt fits for the 245nm rms and 8nm rms data (shown in Figure 8) back into their Gaussian and Lorentzain components the percentage of energy in each can be calculated. For the 245nm rms Voigt fit the Gaussian profile contains 15% of the energy and the Lorentzian profile contains 85% of the energy. The 8nm rms Voigt fit has 52% of its energy in the Gaussian profile and 48% of the energy in the Lorentzian profile. This shows how critical it is to provide an optical quality surface finish at the ends of the fibers in order to minimize the scattering component of an FRD distribution. We fitted a Voigt function to the FRD radial profiles of the cleave data shown in Figure 6 and used the same deconvolving process to calculate the energy in the Lorentzian (scattering) component for each profile. The energy in the Lorentzian component is reduced by 18% when the cleaved end is immersed. This indicates that the cleaved output ends are also significantly contributing to the scattering observed in the FRD distribution. This highlights the need to consider scattering caused by cleaved ends when measuring fiber FRD and when comparing the relative merits of polishing verses cleaving. We believe that a further improvement could be made to the Voigt FRD model by including an additional Bessel term to account for diffraction effects, although for these experimental results the diffraction contribution is relatively small and is neglected. 5. SUMMARY Two methods are commonly used to measure FRD; the cone technique and the parallel laser beam technique. The parallel beam laser method is sensitive to small changes in FRD and previous data has been fitted by a Gaussian model which appears to accurately describe modal diffusion, however it does not model scattering effectively. We have developed an alternative FRD model for the parallel laser beam technique which includes the contributions from scattering and modal diffusion. It is consistent with scattering inducing a Lorentzian contribution and modal diffusion inducing a Gaussian contribution. The convolution of these two functions produces a Voigt function, which is shown to better simulate the observed behavior of the FRD distribution and provides a greatly improved fit over the Gaussian model. Because our model is based on physical processes happening within the fiber it can be deconvolved to quantify the contributions from the Gaussian and Lorentzian components, and in principal the model could be adapted to include diffraction effects. Therefore this Voigt FRD model is a valuable diagnostic tool allowing astronomical instrument scientists to identify, quantify and potentially minimize the various sources of FRD, thereby improving the fiber and instrument performance. Proc. of SPIE Vol U-7

8 ACKNOWLEDGMENTS The authors wish to thank Simon Ellis, Scott Smedley, Will Saunders, Rob Sharp and Scott Croom for their invaluable input. REFERENCES [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] Parry, I. R., Optical fibres for integral field spectroscopy, New Astron. Rev. 50, (2006). Esperanza, C. and Parry, I. R, A method for determining the focal ratio degradation of optical fibres for astronomy, MNRAS 271, 1-12 (1994). Angel, J. R., et al., A very large optical telescope array linked with fused silica fibers, ApJ 218, (1977). Gray. P. M., Fibre optic coupled aperture plate (FOCAP) system at the AAO, Proc SPIE 445, (1984). Kelz, A. et al, Prototype development of the Integral-Field unit for VIRUS, Proc. SPIE 6273, 62733W (2006). Schmoll, J., Popow, E. and Roth, M. M., Focal-Ratio Degradation Optimization for PMAS, Fiber Optics in Astronomy III, PASP 152, (1998). Avila, G., Singh, P. and Albertsen, M., Photometrical scrambling gain and focal ratio degradation in fibers for astronomical instruments, Proc. SPIE O (2006). Oliveira, A. C., de Oliveira, L. S. and Santos, J. B., Studying focal ratio degradation of optical fibres with core size of 50µm for astronomy, MNRAS 356, (2005). Poppett, C. L. and Allington-Smith, J. R., Fibre systems for future astronomy: anomalous wavelength-temperature effects,, MNRAS 379, (2007). Lee, D., Haynes, R. and Skeen, D. J., Properties of optical fibres at cryogenic temperatures, MNRAS 326 (2), (2001). Ferwana, S., et al., All-silica fiber with low or medium OH-content for broadband application in astronomy, Proc. SPIE 5494, (2004). Haynes, R., et al., New age fibers: the children of the photonic revolution, Proc. SPIE 5494, (2004). Gloge, D., Optical Power Flow in Multimode Fibers, Bell Sys. Tech. 51, (1972). Proc. of SPIE Vol U-8