Comparison of FRD (Focal Ratio Degradation) for Optical Fibres with Different Core Sizes By Neil Barrie

Transcription

1 Comparison of FRD (Focal Ratio Degradation) for Optical Fibres with Different Core Sizes By Neil Barrie Introduction The purpose of this experimental investigation was to determine whether there is a dependence of focal ratio degradation (FRD) and throughput on the core size of a fibre. This would then allow us to deduce whether core size should be considered when choosing fibres for astronomical instruments, because typically when deciding which fibres to use the scale of the field plate is the deciding factor rather than the optical properties of the fibre. FRD (a decrease in focal ratio between the input and output) is a major cause of losses in astronomical instruments, mainly on entry to the spectrograph. Due to low intensity light involved in astronomy, any light or information loss should be minimised We also attempted to determine how well the black reimaging tubes perform as an optical system when put together by screwing the tubing together without further adjustment. The black reimaging tubes are commonly used in optical systems, yet there has not been much investigation into how efficient they are in optical set-ups. Theory An optical fibre is a very pure glass fibre which acts as a waveguide allowing light to propagate and be contained along its length. A stepped index fibre consists of 3 main layers: a core where the light propagates and is contained in the fibre via total internal reflection, a cladding which has a lower refractive index than the core allowing total internal reflection to occur, and an outer buffer which protects the fibre from damage. Total internal reflection occurs when light is incident on the surface of a material of lower refractive index than the initial medium and its angle of incidence is greater than the critical angle (which is determined by the ratio of the refractive indices of the two mediums), the light completely reflects from the surface boundary. The critical angle can be determined using Snell s Law to get θ Crit (1) This is utilised in optical fibres, where light continually undergoes total internal reflection inside the core of the fibre. The refractive indices of the cladding and the core are very close, so the critical angles for optical fibres is quite high. If the light has to be incident on the core/cladding boundary such that the angle of incidence is larger than critical angle, it will be able to be contained in the core (via total internal reflection). This means that there is a limit on the angle at which light can enter the core of a fibre and still be contained in the core of the fibre; this is known as the acceptance angle. The acceptance angle can be determined using the following equation (2), where θ is the acceptance angle Also assumes the fibre is in air. This can then be extended to the idea of an acceptance cone, which describes all the light that can enter the fibre and still be contained by in the core. As shown below in figure 1. Figure 1. Diagram showing the path difference between light rays entering the acceptance cone, and those that enter outside the acceptance cone; and also the basic structure of a stepped index fibre

2 The sizes of these acceptance cones are generally described and compared using the corresponding numerical aperture (NA) or f-number (or focal ratio). The numerical aperture of a fibre, input or output, is given by NA=nsin(θ) (3) where θ is the angle between the boundary of the cone and the fibre axis (the half angle of the cone), and n is the refractive index of the medium the fibre is situated in (i.e. if just air NA=sin(θ) as n is approximately 1). It is a dimensionless number. F-number is used to describe the diameter of the input cone of light compared to the focal length of the lens, and is expressed in the form f/#, where # is the ratio between the lengths between the effective aperture size and the focal length (f/d). Higher f-numbers correspond to smaller effective aperture sizes. (E.g. If the f-number is f/2 then the diameter of the aperture is half the length of the focal length of the lens, and f/4 has an aperture diameter a quarter of the focal length. f/4 is a higher f-number than f/2). The relationship between f-number and numerical aperture is given by the approximation (which is good for low NA) f/# (4) The different angles at which light can enter into a fibre give rise to the different modes (distributions of the wave in the fibre) which can propagate down the core of the fibre. Each mode has a distinct distribution in the fibre. They can be determined by using geometric optics for optical fibres with large cores (by treating modes as separate rays); but when a fibre has a core diameter less than about ten times the wavelength of the light propagating through it, the modes must be determined by solving Maxwell's equations, with the core/cladding boundary determining the boundary conditions. The number of modes is dependent on the size of the core, the NA (of the fibre or the input light) and the wavelength of the light to be propagated through the fibre. This relationship is shown by the equation (5) where a is the fibre s core size, the fibre. is the wavelength of the incoming light, and NA is the numerical apeture of Single mode fibres (SMF) are optical fibres that have small enough cores and NA's such that only the propagation of a single mode in their core is possible. This mode is the lowest order mode possible, which travels parallel to the length of the fibre. Multi-mode fibre s (MMF) have higher NA s and larger core size, which means that more modes can propagate in the core (can be seen in equation 5). A fibre can be a SMF for given wavelengths, but for shorter wavelengths more modes may be able to propagate inside the core of the fibre. So whether a fibre is SMF or MMF is dependent on the light entering it. This can be seen in equation 5 where N is inversely proportional to the wavelength entering the fibre. For example, a fibre that is a smf in the infrared will be able to have multiple modes propagate in it's core when using visible light. A major cause of information loss in astronomical applications which use optical fibres is focal ratio degradation (FRD). This is the optical effect in which the size of the output cone of light emitted from a fibre is larger than the input cone. This corresponds to an increase in NA (NA up-conversion), or a decrease in f-number between the input and output. This is important to consider in astronomical instruments because having an FRD too high can cause information loss on entry to the spectrograph (because there is a max light cone accepted by the spectrograph), and loss of the angular distribution of the input light. In astronomical applications you are only dealing with low levels of light, so any losses are incredibly detrimental to the output results. The main causes of FRD in optical fibres are: scattering due to fluctuations in density and composition in the core (compositional irregularities), variations in core diameter along the length of the fibre, imperfections at the core to cladding interface, mechanical deformation (a change in the geometry of the fibre, due to micro and macro bending), imperfections on the ends of the fibre (bend light as it exits the fibre), overfilling or under filling the acceptance cone can cause increased losses (i.e. high input f-ratio leads to higher FRD), and Rayleigh scattering. When there is more power in the higher modes there is more FRD. This is because higher modes are more susceptible to scattering due to imperfections or changes in the fibre geometry (micro-bending), as they travel further through the fibre the low order modes. This is why it is expected that blue light going into a fibre will have higher FRD as there is more energy in higher modes, compared to red input light.

3 The higher order modes in MMF s cause the most problems in reference to increased FRD. This is because higher order modes travel further along the length of the fibre, so are more likely to be affected by scattering or absorption compared to lower modes. This can also leads to modal stripping, where certain high order modes are removed from the core of the fibre due to interactions with the medium. Due to scattering cladding modes can be produced, causing higher FRD s to be measured. Modal dispersion also has a major effect on the image quality of the output of a fibre. Modal dispersion is the process in which a transmission is distorted due to different mode propagation velocities in a fibres core. Different modes that enter the fibre at the same time may exit at later times as higher order modes (lower propagation velocities) have to travel further along the fibre. Different modes are produced by the light signals entering the fibre via different angles in relation to the fibre axis, so the larger the angle (until the critical angle) the slower the propagation velocity. This effect has a major impact on the output of a multimode fibre, due to its many modes. As the length of the fibre increases, so does the effect of modal dispersion as they delay in the exit between higher and lower modes will be larger. The initial modal distribution in the fibre is dependent on the source and intermediate components, so the amount that the output is affected by modal dispersion relies a lot on these factors. We used a blue and a red Bessel filter, with peak wavelengths of around 450nm and 650nm respectively. As λ decreases (blue to red) the number of modes increases. This means that when the blue filter is applied more high order modes will be able to propagate in the fibre compared to the red, and hence more modal dispersion and FRD will occur. Higher modes have to travel further through the fibre, meaning that they have a higher chance of being affected by imperfections in the fibre or mechanical stress compared to those in lower modes. Using formula 5, a quick calculation shows that the amount of modes for the blue filter will be over double ((650/450) 2 =2.09) the amount of modes for the red filter. Experimental set-up and Method: The optical system used for this experiment used a 10 μm core SMF (in the infrared) as the input, which is not a smf in the visble, but a few mode fibre. This input fibre had light from a LED source incident on it. Between the fibre and the LED was placed a red or blue Bessel filter, which allowed certain wavelengths to be chosen for the input light. The input fibre was placed in a fibre holder and screwed into the black reimaging tubing. This was placed approximately 75mm from a 75mm focal length plano-convex lens (flat side facing the expanding beam) such that light from the fibre will pass through the lens and be collimated. We collimated the beam, emerging from the 75mm lens, by taking pictures of it with a CCD at varying distances from the lens. If the beam is collimated correctly the images should be the same size at any distance from the collimating lens. The collimated beam was then passed through an iris (4-12mm diameter) which allows a certain input NA (or f- number) to be chosen, by varying the diameter of the beam. This light was then incident on a 35mm focal length plano-convex lens (convex side facing the collimated beam), which focuses the beam onto the end of the test fibre that is approximately 35mm away. Initially we tried to find the focus by taking images using the CCD camera, which was mounted on a movable stage with a micrometre, allowing the camera to stay aligned and enable small distance adjustments. We would then analyse the spot profiles at various distances from the focusing lens to find the smallest spot size possible. The best spot size obtained was 16 pixels (144 μm) at 1%, 4 pixels (36 μm) at 10%, and 1.5 pixels (13.5 μm) at FWHM (Full Width Half Maximum). We also took back focus (1.5mm back from the focus) images at this stage, which would allow us to calculate the throughput and FRD for each fibre, filter and input NA, but the images taken were incorrect, so we could not do this.

4 Figure 2. A photograph of the optical system we constructed using the black reimaging tubes, with the microscope used to align the focused beam with the end of the test fibre. The test fibre was then cleaved, and mounted in a fibre holder on the stage at approximately the right position such that the focus of the beam was on the fibre holder. The fibre holder was initially aligned with the system by connecting it to the main setup with tubing, and then removing the tubing. Once the fibre was in position we used a microscope to attempt to place the focus on the centre of the test fibre by adjusting the screws on the fibre holder, which allowed us to alter its horizontal and vertical positions in reference to the focus spot (as shown in figure 2). Figure 3. Diagram representing the experimental set up used

5 The other end of the test fibre was cleaved and aligned in a v-groove, which was on a movable stage, in front of the camera setup, ready to image the output. All cleaves were checked, using the magnification of the viewing window of the splicer, before being placed in the set-up, to ensure the best results. This is important as poor cleaves would have caused increased FRD and decreased image quality. Once each end was mounted we used the moving stage to alter the position of the fibre in reference to the camera until it was in line with the designated centre pixel of the camera, by moving the stage in the vertical and horizontal directions (the camera was in the focus position for this). After being centred we then attempted to find the focus by moving the fibre along the cameras axis, until the smallest spot was found. The camera was then moved into back focus (1.5mm away from the focus position) and images were taken for each aperture size and filter, followed by taking dark images. The fibres were to be tested at the following input f numbers (or NAs), to corresponding input aperture diameter (the input f-numbers were altered by adjusting the iris size): Table 1: Input f-numbers and NAs for a given aperture size. Input Aperture Size (mm) F-Number f/2.9 f/3.2 f/3.5 f/3.9 f/4.4 f/5 f/5.8 f/7 f/8.8 NA These images were then reduced in the program IRAF by Julia, and we then plotted them in excel. This method and set-up was to be used to test and hence compare the three AFS fibres. The fibres to be tested had a length of approximately 20 m, they had core/cladding sizes of 50/125 μm, 105/125 μm, and 200/220 μm, and each had NAs of There were various factors that contributed to the errors in the output measurements. These were the alignment of the v-groove plate with the optical axis (and how the fibre sits in it), the alignment of the camera, and the focusing of the output fibre. The errors for the alignment of the camera and the focusing of the fibre were previously determined by Julia to be < ±0.001 and ±0.007, respectively. The error for the alignment of the v- grooves was determined by shifting the v-groove plate along the optical axis and measuring the change in the centre of the output image. This kind of error can be caused by how the fibre sits in the grooves and the quality of the end cleave. All errors together give a total measurement error of ±0.01 (for NA). Results The results below are for the 50 μm core fibre which was imaged by the CCD camera for each aperture size with the blue and then the red filter applied. Darks were taken and subtracted from the images by IRAF, and the data was then reduced in IRAF by Julia Bryant using a custom reduction package based on IRAF routines. Figure 4 shows that there is higher output NA (for a given encircled energy) when the blue filter is applied compared to when the red filter was applied. As this includes every aperture size (for the blue and red filters), it also shows that the changing of the aperture size did not have much effect on the NA recorded for a given encircled energy.

6 Encircled Energy (%) Encircled Energy (%) Red vs Blue for 50 μm Core Fibre Numerical Aperture Figure 4. A comparison of the encircled energy vs numerical aperture graphs for both the blue and red filters, including each aperture size; for the 50 μm core fibre. Colour represents the applied filter. The outputs of each aperture size with the red filter applied (shown in figure 5) approximately follows the trend that, decreasing aperture size leads to higher NA at a given encircled energy. Although the uncertainty in the NA measurement is greater than the difference between the smallest and largest output measurement. So each aperture size produced an output that has about the same NA, within errors μm Core Fibre (Red Filter) 4 mm 5 mm 6 mm 7 mm 7 mm b 8 mm 9 mm Numerical Aperture 10 mm 11 mm 12 mm Figure 5. A comparison of the encircled energy vs numerical aperture graphs each aperture size for the red filter, for the 50 μm core fibre

7 Encircled Energy (%) The outputs of each aperture size with the blue filter applied (shown in figure 6) approximately follows the trend that, increasing aperture size leads to higher NA at a given encircled energy. Although similarly for figure 5, the uncertainty in the NA measurement is greater than the difference between the smallest and largest output measurement. So each aperture size produced an output that has about the same NA, within errors μm Core Fibre (Blue Filter) 4 mm 5 mm 6 mm 7 mm 7 mm b 8 mm 9 mm Numerical Aperture 10 mm 11 mm 12 mm Figure 6. A comparison of the encircled energy vs numerical aperture graphs each aperture size for the blue filter, for the 50 μm core fibre We did not obtain any results for the 105/125 μm or the 200/220 μm fibre, because the 105 μm core fibre was deemed faulty, and the 200 core was not able to be cleaved at the time as the required equipment was not available. Although the input back focus images were not fit use to determine the throughput (as they were not correct), it can still be seen in figure 6, that the iris was working as intended. This is an image of the 4mm aperture image subtracted from that of the 12mm aperture image. Figure 7. This is an image of the subtraction of the 4mm back focus input image from that of the 12mm back focus image. It can clearly be see that the iris is performing as required, and hence the input should have the correct aperture size (NA)

8 Encircled Energy (%) From Figure 6, the NA values for each input aperture can be approximated by assuming that the middle black spot represents the 4mm, and then extrapolating how many pixels it is to the other aperture sizes. The list of NAs in order from the 12mm to 4mm aperture sizes is: 0.186, 1.71, 0.155, 0.140, 0.125, 0.11, 0.094, 0.079, Plotting these values gives the graph in Figure 8, which illustrates the expected NA progression for each aperture size. The NA differences between each aperture size in this data are much larger than those found in the experimental data. Although the purpose of this graph is to show the expected positions of the input and output NAs relative to the aperture sizes, not to give any quantitative information. Predicted Relative Encircled Energy vs NA for the Input 4mm 5mm 6mm 7mm 8mm 9mm 10mm 11mm 12mm Numerical Aperture Figure 8. A comparison of the relative predicted encircled energy vs NA of the input profile, for each aperture size. The actual profiles would not be completely straight like this, but curved with a profile dependent on the input light profile; this is just to show the relative NA differences expected between each output. We had many problems with the CCD camera used to take the output images, which caused many time delays. Figure 9a and b shows the state the camera was in once we got it to start working. The condensation was inside the CCD camera, and caused the output images of the fibres to be useless, so we were not able to obtain any useful images until this had cleared.

9 Figure 9a. An image taken with the CCD camera which shows the condensation formed on it. Figure 9b. A close up of the water droplets showing in the CCD camera image.

10 Discussion The results from the 50 μm core fibre provided various interesting results, but if we had been able to test the other two fibres, we may have been able to make various comparisons. From figures 5 and 6 it can be seen that each of the outputs (for the 50 μm core fibre) for each aperture size is very close together, such that they are all within each other s uncertainty. Comparing this with the expected trend for the inputs in figure 8 clearly shows that the FRD must have increased with increasing input size of the aperture; i.e. smaller aperture sizes (smallest NAs) suffer worse FRD. This trend agrees with what we expected. The outputs (for the 50 μm core fibre) for the blue light were mostly in the expected order in reference to the input NA s (similar to the order represented in figure 8). Although for the red filter results the trend is the opposite with the NA approximately increasing with decreased aperture size, which is not expected. Yet each of the outputs was very close together, with the differences between them being less than the error in the NA, so this is not significant. Although the fact that all the outputs overlapped for both the red and blue filters was unexpected, this may have been due to the poor quality in the input beam, which may have been due to lack of precision in the black reimaging tubes when simply screwed together, leading to less than desired accuracy in the collimation and focusing. As expected when the blue filter was applied the output NA for a given encircled energy was higher than that for the red filter. Although the difference isn t large there is still a clear trend. This is expected because blue light has a shorter wavelength compared to red light, which means it has more modes (as can be seen in equation 5). Higher modes are more susceptible to scattering due to them having to travel further through the fibre compared to lower order modes. This means that they contribute more to FRD, than lower modes. Unfortunately are input back focus images were incorrect so we were not able to get quantitative results for the output FRDs or throughput for the 50 μm core fibre. Although, it can be seen in figure 7 that the iris was working as intended. The input images may have been poor because of problems with the optical system or the collimation, or that we did not have the CCD camera in the correct position to take the back focus images (1.5mm back from the focus). The last one is a possibility because it is quite difficult to find the exact focus position when the input light is from a multimode fibre, because the light does not exit the input fibre from a set focal point. This means there is an effective lengthening of the focus. The input spot size may have also had an impact on the results found for the 50 μm core fibre outputs. The optical set-up we put together should have demagnified the size of the spot at the input (approximately 10 μm) to a size of factor 35/75 smaller (ratio of the two lens in the system). This was not achieved with the best spot found having a size of 144 μm at 1%, 36 μm at 10%, and 13.5 μm at FWHM. This vast discrepancy is most likely due to poor alignment, collimation and/or focusing. There was also the problem of there being no distinct focal point, as described above. This made it a lot more difficult to find the focus and probably caused less than desired precision. If the cleave of the ends of the test fibres is incorrect, or imperfect, the FRD measured can be affected. This is because imperfections in a cleave can cause light to exit the fibre at different angles to what it ideally should. This can then lead to higher FRD s as it is possible for the light to exit or enter at higher angles than possible, with an ideal cleave. So multiple cleaves should be taken and tested in order to ensure bad data is not obtained due to poor cleaves. Any data that is completely inconsistent with other cleaves can be removed, as being caused by a poor cleave. If not for time constraints we should have tested the 50 μm with multiple cleaves. We experienced various problems during this experimental investigation, which had many impacts on the quality of our results and also our ability to get results. These led to us being unable to achieve the goals we initially set. One of the major problems encountered during the experiment was that the output imaging CCD camera was not operating up to standard when it was needed. To begin with there was a problem with the communication between the camera and the computer. So we attempted to get the camera functioning by loading new drivers and software, tweaked the settings, and changing the computer it was connected to. When the camera did start working the images produced were almost useless, because there was water droplets condensed in front or on the imager itself (as shown in figure 9a and b). At one stage it did start working temporarily, and there was no condensation affecting the images. This enabled us to get data for the 50 μm core fibre, and also test, and hence

11 determine that the 105μm core fibre was faulty. This caused major delays in our experiment and subsequently we obtained a limited amount of results. The 105 μm core fibre was deemed faulty due to the poor results it gave. The results for the 105 μm core were shifted far to the right (way beyond expectations) of the 50 μm on the encircled energy vs numerical aperture graphs, when used in both our setup and the finely tuned setup. A shift to a higher NA in reference to the 50 μm results was expected due to its larger core size, which means the 105 μm fibre has many more high order modes compared to the 50 μm core fibre (as can be seen in equation 5);. This means that this fibre should suffer higher FRD. The extent to which it had shifted was beyond our predictions. The cleaves were also checked for imperfections, and found to be useable. Both of these pieces of evidence indicated that something must be wrong with the fibre itself as it would be expected to have worse FRD but not to the same extent. We narrowed down the problem to being either defect in the manufacturing of the fibre, or it had been wound to tightly in its packaging; we did not have time to determine the cause. The 200/220 μm was not able to be tested as we were not able to get access to the equipment required to cleave it. It could not be cleaved due to the large size of the fibre. The cleaver that was required to effectively cleave the fibre was the Vytran cleaver, which was being used by others at the time of our experiment. Also, we were not able to get conclusive results on whether the black reimaging tubes are suitable for accurate optical systems, due to not being able to have more comparisons. Although if we had found problems, it s possible that they may have been caused by not having the required precision in collimating our beam, aligning the fibres and tubing, and in the focusing of the light on the end of the test fibre. Conclusion: Due to time limitations and equipment problems we were not able to complete are initial goals, but we were still able to collect data for both the 50 and 105 µm core fibres. The results for the 50 µm core fibre exhibited the expected trend for the difference in FRD between the blue and red light inputs; i.e. blue suffering a higher NA up-conversion. The results also indicated that higher focal ratio inputs produced higher FRD in the outputs. Although, the results for the 105 µm were very bad in both set-ups indicating the presence of either a manufacturing defect, or that the fibre was wound to tightly in its packaging. With more time we may have been able to undertake further tests, and gained enough results to make more comparisons and conclusions. There were various tests we did not get to complete due to lack of time. Such as we did not get to cleave or test the 200/220 μm fibre, and the 105/125 μm was faulty. This meant that we did not have the ability to compare the relative FRDs of each fibre. To do this in future we would need access to the Vytran cleaver, and a replacement 105/125 μm fibre. In this test multiple cleaves should also be done, in order to get the best results, and see what effect it has. The goal to compare the quality and efficiency of the black reimaging tubes to that of a finely tuned set-up could also be further tested if each of the different sized core fibres is able to be tested. Back focus images of the input would also help with this as the two inputs can be compared between the two systems, as well as provide quantitative values of FRD for comparison, and also throughput measurements. References: Title: Hexabundle lab test results as applicable to MANIFEST Author: Julia Bryant Title: Focal ratio degradation in optical fibres of astronomical interest Author: Ramsey, L. W. Title: The dependence of the properties of optical fibres on length Author: C. L. Poppett and J. R. Allington-Smith