Coherent hollow-core waveguide bundles for thermal imaging

Transcription

1 Coherent hollow-core waveguide bundles for thermal imaging Udi Gal, 1,3 James Harrington, 2,4 Moshe Ben-David, 1,5 Carlos Bledt, 2,6 Nicholas Syzonenko, 2 and Israel Gannot 1, * 1 Department of Biomedical Engineering, Faculty of Engineering, Tel Aviv University, Tel Aviv 69978, Israel 2 Department of Material Science and Engineering, Rutgers University, Piscataway, New Jersey 08854, USA 3 Udi.Gal@nuvoton.com 4 jaharrin@rutgers.edu 5 Moshe.ben david@gmail.com 6 cmbledt@eden.rutgers.edu *Corresponding author: gannot@eng.tau.ac.il Received 15 March 2010; revised 23 July 2010; accepted 28 July 2010; posted 4 August 2010 (Doc. ID ); published 24 August 2010 There has been very little work done in the past to extend the wavelength range of fiber image bundles to the IR range. This is due, in part, to the lack of IR transmissive fibers with optical and mechanical properties analogous to the oxide glass fibers currently employed in the visible fiber bundles. Our research is aimed at developing high-resolution hollow-core coherent IR fiber bundles for transendoscopic infrared imaging. We employ the hollow glass waveguide (HGW) technology that was used successfully to make single-hgws with Ag/AgI thin film coatings to form coherent bundles for IR imaging. We examine the possibility of developing endoscopic systems to capture thermal images using hollow waveguide fiber bundles adjusted to the 8 10 μm spectral range and investigate the applicability of such systems. We carried out a series of measurements in order to characterize the optical properties of the fiber bundles. These included the attenuation, resolution, and temperature response. We developed theoretical models and simulation tools that calculate the light propagation through HGW bundles, and which can be used to calculate the optical properties of the fiber bundles. Finally, the HGW fiber bundles were used to transmit thermal images of various heated objects; the results were compared with simulation results. The experimental results are encouraging, show an improvement in the resolution and thermal response of the HGW fiber bundles, and are consistent with the theoretical results. Nonetheless, additional improvements in the attenuation of the bundles are required in order to be able to use this technology for medical applications Optical Society of America OCIS codes: , Introduction /10/ $15.00/ Optical Society of America Thermal endoscopic systems not only could provide useful information concerning abnormalities in spaces within the body, but also could have other applications, such as in emergency rescue situations. In this paper, we examine the possibility of developing endoscopic systems to capture thermal images using hollow waveguide fiber bundles adjusted to the 8 10 μm spectral range and investigate the applicability of such systems. Recent advances in infrared light detectors, the development of new materials for IR fibers, and improvements in the IR electronic 4700 APPLIED OPTICS / Vol. 49, No. 25 / 1 September 2010

2 endoscopic system should lead to the development of endoscopic systems for thermal images with the required temperature resolution in the near future. Coherent fiber optic arrays composed of oxide glass fibers have been fabricated for many years, using mandrel wrapping and leached bundle technologies [1]. These coherent fiber bundles have been used to transmit high-resolution images for a variety of applications, including endoscopic medical imaging of tissue and industrial borescopes for remote inspection systems. There has, however, been very little work done to extend the wavelength range of fiber image bundles to wavelengths greater than 2 μm. This is due, in part, to the lack of IR transmitting fibers with optical and mechanical properties analogous to the oxide glass fibers currently employed in the visible fiber bundles [2]. Nevertheless, coherent fiber bundles for the IR range could have significant thermal imaging applications, especially for temperatures in which human body radiation is most intense. To date, most IR fiber arrays have been fabricated from chalcogenide glass fibers. Nishii et al. [3,4] and Hilton [5] have made coherent IR fiber bundles consisting of several thousand As 2 S 3 fibers. These chalcogenide glass fibers are transmissive from about 2 to 5 μm. For efficient IR imaging with clinical value, we would like to have fibers that transmit up to at least 14 μm because the thermal energy of tissue near room temperature is at a maximum near 10 μm. Therefore, the use of IR fibers with a broader IR wavelength range means more signal and greater temperature differentiation within the image. Additionally, the As 2 S 3 fibers are quite fragile and easily damaged during use. Finally, the chalcogenide glass fibers used in the bundles contain absorption bands due to impurities that limit the IR transmission. More recently, Katzir et al. [6 8] extruded polycrystalline silver halide fibers into coherent bundles. Their silver halide bundles, however, are of poor optical quality, as they are made by an extrusion process that tends to deform the soft halide fibers and distort the resultant image [9]. We report the use of hollow glass waveguide (HGW) technology that we have used successfully to make single HGWs [10] with Ag/AgI thin film coatings to form coherent bundles for IR imaging [11]. This HGW technology is well-established for the single hollow waveguides. In fact, the Ag/AgI HGW technology has been used for fabricating commercially available waveguides for sensing and power delivery applications. It is this simple and straightforward methodology that is used for coating the hollow collimated hole structure. The hollow oxide glass bundles that we use in this research are more robust, as they are made from the same glass customarily used to make the solid-core oxide glass fiber bundles. Another advantage of fabricating an image bundle using hollow-core waveguide bundles compared to solid-core fibers is that we may employ the same fiber bundling techniques used to make oxide glass image guides. These techniques, which involve either mandrel wrapping or leach bundles/fiber redrawing, are very well-established. In addition, we do not need to coat the tubing prior to forming the bundle, and in this way, we ensure that the coatings are not damaged during any type of bundling process. Instead, once the bundle has been fabricated, we coat all tubes simultaneously with metal and dielectric coatings. The hollow oxide glass structure that we use is simple in design, low in cost, and quite rugged. 2. Fabrication of Rigid, Coherent HGW IR Bundles A. Fabrication Process One of the most popular hollow waveguides today is the HGW. This hollow glass structure has an advantage over other hollow structures because it is simple in design, extremely flexible, and, most important, it has a very smooth inner surface. HGWs have a metallic layer of Ag on the inside of silica glass tubing and then a dielectric layer of AgI over the metal film to produce a highly reflective inner layer. Figure 1 shows a cross section of the structure of the HGWs. Recently, the technology developed to fabricate single HGWs was extended to produce coherent fiber optic arrays for thermal imaging [11]. The fabrication of HGWs begins with silica tubing, which has a polymer (UV acrylate or polyimide) coating on the outside surface. A wet-chemistry technique similar to that used by Croitoru and his coworkers [10] is employed to first deposit a silver film, using standard Ag plating technology. Next, a very uniform dielectric layer of AgI is formed through an iodization process in which some of the Ag is converted to AgI. The experimental setup for the Ag/ AgI coating procedure is shown in Fig. 2. This procedure has been well-documented in the literature for both single- and multiple-bore waveguides [2]. In brief summary, the silvering solution is composed of AgNO 3 dissolved in distilled water mixed with NH 4 OH and NaOH. The reducing solution used to precipitate metallic silver contains dextrose and Na 2 EDTA in distilled water. The silvering time is 6 to 7 h, which is much longer than the typical 1 h silvering time for single-bore waveguides. The silvering is followed by an iodization of some of the Ag layer to form AgI. The iodine solution is made up of iodine dissolved in cyclohexane. Iodization times vary from 60 to 240 min. Fig. 1. Structure of a Ag/AgI coated hollow glass waveguide. 1 September 2010 / Vol. 49, No. 25 / APPLIED OPTICS 4701

3 Fig. 2. (Color online) Wet-chemistry method for the deposition of Ag (left) and AgI (right) thin films inside silica tubing. B. Structure of the HWG Coherent Bundles The coherent bundles were fabricated by Collimated Holes from soda-lime/lead glass capillaries. We have coated bundles with 50, 75, and 100 μm bore sizes and lengths up to 30 cm. The structure of the bundle is shown in Fig. 3 along with a photomicrograph of a few of the coated tubes. The 50, 75, and 100 μm borecollimated hole bundles have outer diameters of 3, 3, and 4 mm and are composed of 900, 675, and 675 capillary tubes, respectively. The active area of the bundles varies from 42% for the 75 and 100 μm bore HGWs and 35% for the 50 μm bore guides. C. Spectral Response of the HWG Coherent Bundles The spectra for an 8 cm long, 100 μm bore collimated bundle is shown in Fig. 4 for AgI coating times at intervals of 60, 120, 180, and 240 min. The attenuation peaks in the spectra result from interference effects due to the thin AgI films. The longer the iodization coating time, the thicker the AgI layer and the further the shift of attenuation peaks to longer wavelengths. From Fig. 4, we see that the first absorption peak shifts from about 2.5 to 5 μm. From the data in Fig. 4, it is possible to extract information on the kinetics of AgI film deposition, which is useful in tailoring the optical response of the guides. For the optimal guide, the Ag layer is about 1 μm and the AgI thickness is about 0:8 μm. In Fig. 5, we plot the position of the first absorption peak shown in Fig. 4 with respect to the iodization time. The data in Fig. 5 show that the AgI film thickness increases linearly with increasing iodization time. 3. Optical Properties of the Coherent HGW IR Bundles We carried out a series of measurements in order to characterize the optical properties of the fiber bundles. These included the attenuation, resolution, and temperature response. We also developed theoretical models and simulation tools that calculate the light propagation through the HGW bundles and can be used to calculate the optical properties of the fiber bundles. Fig. 3. (Color online) Cross section of coherent bundle showing hexagonal shape of drawn tubing (left) and microphotograph of one capillary with Ag/AgI coating (right) APPLIED OPTICS / Vol. 49, No. 25 / 1 September 2010

4 Fig. 4. (Color online) Spectra of progressively coated 100 μm bore waveguides as measured by Fourier transform infrared. From top to bottom, the waveguides are 60, 120, 180, and 240 min at the right side of the graph. A. Attenuation One important parameter of the fiber bundle is its total attenuation per unit length. The attenuation per unit length of the bundles was measured for two sets of fiber bundles; the first set (D) was optimized for transmitting IR radiation at 4 μm (as seen in Fig. 4), and the second (U) was optimized for the 8 10 μm wavelength range. All the measured fiber bundles had a 100 μm core diameter, the same number of waveguides (675), and the same fill factor (42%). We calculated the attenuation per unit length using the following equation: A ¼ 10 logðp out=p in Þ ½dB=mŠ; L ð1þ where P in and P out are the average irradiance levels at the input and the output facets of the bundle, respectively, and L is the bundle length. To measure the ratio P out =P in, we used a CO 2 (Sharplan, Fig. 5. (Color online) Correlation of position of first absorption peak with iodization time. 1 September 2010 / Vol. 49, No. 25 / APPLIED OPTICS 4703

5 Table 1. Experimental Results of the Attenuation of Radiation through the Fiber Bundles Measured Using CO 2 Laser Radiation Transmitted through the Bundles Bundle Length (cm) P in (watt) P out (watt) Attenuation (db) Attenuation (db=cm) D D U U U U Yokneam, Israel) laser source configured to emit 0:5 W of laser output power. The laser beam was focused using a ZnSe IR lens (f ¼ 5 cm) onto the bundle s face. The input power was reduced to 0:42 W due to the focusing lens attenuation, and, after taking the fill factor into consideration, the actual input power to the bundle was 0:18 W. The spot size covered most of the bundle proximal surface. Table 1 shows the experimental results for each measured fiber bundle. The average attenuation per unit length was 2:35 db=cm for the first set of fiber bundles, and 0:48 db=cm for the second set of fiber bundles. These results clearly show the improvement in the fabrication process and the ability to adjust the dielectric layer thickness to the required wavelength. Matsuura et al. [12] showed that the loss for the best 250 μm single-bore HGWat 10:6 μm is about 2:0 db=m. Decreasing the bore size by a factor of 2.5 to 100 μm would lead to an increase in the attenuation by 2.5 [4] to a value of about 32 db=mor0:32 db=cm. This theoretical value validates our experimental result of 0:48 db=cm and gives us confidence in the fabrication process. B. Resolution Theoretical Background The resolution is normally stated as the number of lines per millimeter that can be transmitted through a bundle. The mathematical tool used for defining the resolution is the modulation transfer function (MTF). We would like to be able to theoretically estimate the MTF of our fiber bundles. One approach is calculating the MTF by first obtaining the system s response to an impulse, called impulse response or point spread function (PSF). The bundle s MTF is the absolute value of the optical transfer function (OTF), which is the Fourier transform of the PSF [13]. Croitoru et al. developed a comprehensive theoretical model to describe mid-ir radiation propagation through an optical cylindrical hollow waveguide [10]. Based on that model, we developed a computer simulation that can calculate the propagation of a light beam through a single hollow waveguide. In order to evaluate the bundle PSF, we assumed a point light source located at one end of the bundle. For each waveguide in the bundle cross section, the entrance angle and energy of light were calculated (described in the next paragraph), and a simulation was done to obtain the energy of light at the distal end of each waveguide. Given a single point source, which is located at a distance X from the fiber bundle on the bundle center axis, rays of light emitted from the point source will enter each fiber in the bundle, but each waveguide will receive the light at different entrance angles and energy levels. A waveguide located close to the center will receive higher energies of light with a very small divergence angle, while waveguides located far from the center will receive lower energies of light at a larger angle (as can be seen in Fig. 6). These two factors will cause the energy distribution at the distal end of the bundle to decrease as we go farther away from the bundle axis. As we know, the angle at which light enters the fiber strongly influences the attenuation of the propagating light due to the dependency between the entrance angle and the number of times the light collides and is reflected from the fiber surface. We can easily calculate the minimal and maximal angles (β min and β max in Fig. 6), but, if the distance of the point source X is considerably larger then the radius of a single waveguide in the bundle, then a reasonable approximation would be to assume that all the light entering the waveguide is at a single angle β avg, which is the entrance angle in the center of the waveguide. The energy distribution at the distal end of the fiber bundle will also be influenced by the amount of light energy entering each waveguide (P in ). As all the waveguides are of the same radius, the difference in P in between one waveguide to the Fig. 6. (Color online) Light emitted from the source point will travel a different distance and enter each fiber in the bundle at different entrance angles APPLIED OPTICS / Vol. 49, No. 25 / 1 September 2010

6 Fig. 7. (Color online) Left: simulated bundle PSF for 100 μm core fiber bundle. Right: calculated MTF for 100 μm core fiber bundle. next will be determined only by the distance from the light source. If the source is radiating isotropically, the equation for the intensity as a function of radius is given by jij ¼ P 4πr 2 ; ð2þ where P is the net power radiated, I is the intensity at the surface of the sphere, and r is the radius of the sphere. Thus, if we denote the energy of light entering the center fiber (closest to the light source) P in, the intensity at any other waveguide along the cross section would be X 2 P i in ¼ Pin; ð3þ r i where X is the distance of the bundle from the light source, and r i is the distance of the ith waveguide from the light source. The simulation was one dimensional, done for one cross section of the fiber bundle, assuming that it is polar symmetrical for any cross section. The left graph in Fig. 7 shows the simulated fiber bundle PSF for a 100 μm core and 8 cm length fiber bundle. The point light source distance from the bundle surface was 1 mm. The OTF was obtained by Fourier transforming the PSF, and the bundle MTF is the absolute value of the OTF. The right graph of Fig. 7 below shows the calculated fiber bundle MTF, and as the resolution is determined by the width at half-maximum [14], the calculated resolution is 1.9 lines/mm. C. Resolution Experimental Results The MTF is formally defined as the magnitude of the OTF, where the OTF is the response of an imaging system to a spatial pattern whose intensity varies sinusoidally at some spatial frequency. The MTF is a measure of the 2D spatial frequency response of the system (two orthogonal axes: horizontal and vertical). Because our bundles are symmetric, 1D modulation is usually sufficient to characterize the bundle resolution. Because sinusoidal spatial patterns are generally difficult to generate in the infrared range, we used the knife-edge method as described by Tzannes and Mooney [15]. A sharp knife edge is illuminated with an IR laser beam, and its image is formed on the distal end of the bundle. The image is transmitted to the proximal end of the bundle and recorded using a thermal imaging camera (Thermovision A40; FLIR Systems, Boston, Massachusetts) operating in the μm spectral range, with a 2:5 cm focal length magnifying lens between the bundle and the camera. A gray-level line profile is digitally sampled perpendicular to the knife-edge direction, and the result is the edge spread function (ESF). Figure 8 shows the ESF of the fiber bundle as measured using the knife-edge technique. The next step is to obtain the line spread function (LSF) by differentiating the ESF. To avoid numerical Fig. 8. (Color online) Knife-edge response of the bundle and the ESF approximation. 1 September 2010 / Vol. 49, No. 25 / APPLIED OPTICS 4705

7 Fig. 11. bundle. Experimental setup for the thermal response of the fiber Fig. 9. (Color online) MTF of the 100 μm core fiber bundle. differentiation, the ESF is approximated by a polynomial function [14] and analytically differentiated with respect to the scan direction to yield the LSF. Next, we compute the Fourier transform of the sampled LSF. The discrete Fourier transform (DFT) is a 1D profile that is done in the direction perpendicular to the original knife edge. The result is the MTF, and the resolution of the bundle was determined by the width at half-maximum. In our bundles, the resolution was found to be 2.2 lines/mm for a 100 μm core diameter bundle and 8 cm length, as can be seen in Fig. 9. These resolutions are adequate for transmitting goodquality thermal images. Figure 10 below shows the calculated fiber bundle MTF (smooth line), as was calculated in the previous section, and the measured MTF using the knife-edge technique. The calculated resolution is 1.9 lines/mm, and the measured resolution is 2.2 lines/mm. As can be seen, the calculated resolution and the measured one are quite similar. 1. Thermal Response Experimental Results Measuring the thermal response of the fiber bundle required a temperature-controlled target, which can be tuned very accurately to any temperature at the range of at least 200 C. The target we chose was a 0:5 mm thick lead rod connected to a current source. We applied different current levels through the lead rod and observed it with the thermal camera to obtain the exact relation between the electrical current running through the lead rod and its temperature. The lead rod showed a linear and stable relationship between current and temperature, giving us a convenient temperature-controlled target. We placed the temperature-controlled target in front of the distal end of the fiber bundle while focusing the thermal camera on the proximal end. We then changed the target temperature gradually and measured the temperature obtained by the camera. The experimental setup illustrated in Fig. 12 shows the temperature of the target versus the temperature seen by the thermal camera at the proximal end of the fiber bundle. The results show that a notable change in the output temperature starts around 60 C, and from that point onward, the average ratio between temperature changes in the target and the temperature changes in the camera are 20 (for every 20 C change in the target temperature, the camera temperature will change by 1 C). The experimental setup for measuring the minimum resolvable temperature difference (MRTD) with the bar target method is shown in Fig. 13. We used a bar target that is composed of a few black lines of emissivity ε 1, which were painted on a metal plate (of low emissivity ε 0:02). The width w of each line was equal to the separation, u, between the Fig. 10. (Color online) Calculated (smooth) versus actual (jagged) MTF for 100 μm core fiber bundle. Fig. 12. (Color online) Temperature sensitivity of the fiber bundle. The target temperature (blue left y axis) versus the temperature via the fiber bundle (red right y axis) APPLIED OPTICS / Vol. 49, No. 25 / 1 September 2010

8 Fig. 13. Experimental setup to measure the MRTD using the bar target method. lines. We used w ¼ u with a value of 0:4 mm. The imaging resolution is the camera s spatial resolution, which is 1:3 mrad. The camera thermal sensitivity is 0:08 C. As the bar target was uniformly warmed, the apparent temperature of the bars is related to their emissivity value (ability to emit energy by radiation) and does not reflect the true target temperature (which was probably quite similar). In this experiment, the temperature values we report are the apparent temperatures (as seen by the thermal camera) and not the actual target temperature. The bar target was slowly warmed until it was observable via the fiber bundle. At that point, we measured the temperature of the hot (metal) lines to be 55:5 C, and the temperature of the cold (black) lines was 42:3 C. This measurement yields an MRTD value of 13:2 C. The response of our system to a bar target object is shown in Fig. 14. The right-hand side of Fig. 14 shows the bar target as seen directly by the thermal camera; the left-hand side of Fig. 14 shows the image transmitted through the HGW bundle. 4. Thermal Imaging of a Coherent HGW Bundle A. Experimental Setup A small-bore rigid coherent bundle with a capillary bore size of 100 μm and 900 holes was used to image a hot target. The HGWused was optimized to yield the best transmission at an 8 10 μm wavelength range, as described in Subsection 3.A All the images were obtained using a thermal imaging camera (Thermovision A40; FLIR Systems, Boston, Massachusetts) operating in the μm spectral range, with a 2:5 cm focal length magnifying lens between the Fig. 15. Experimental arrangement for IR imaging of a hot wire through the 900 hole, 100 μm bore HGW bundle. The tungsten wire was electrically heated and placed 1 mm in front of the bundle s left end. The image emitted from the bundle s right end was magnified by a 2:5 cm IR lens and the IR camera s close-up lens and recorded by the camera. bundle and the camera. There were no optics between the object and the bundle; the target objects were simply placed very close to the bundle (1 2 mm). The setup is shown in Fig. 15. Figure 16 shows the image transmitted by the bundle. The hot tungsten wire imaged had an outer diameter of 0:2 mm, and the lead rod was 0:5 mm in diameter. The temperature of the wire was about 230 C. The temperature scale in the figure corresponds to the camera s reading after the attenuation caused by the optical coupling. B. Thermal Imaging Results The experimental setup in Fig. 15 was used to capture different images of various warm objects. Figure 16 shows examples of thermal images transmitted by the fiber bundle. The image object consisted of a tungsten wire and a lead rod that were heated by an electric current. C. Simulation of a Thermal Image Transfer through a Fiber Bundle In order to obtain the optical effect of a fiber bundle on a 2D image, we treated each pixel in the source image as a single point light source. In the same way as discussed in Subsection 3.B, a computer simulation calculated the propagation of a light beam through a single hollow waveguide. For each pixel in the source image and for each waveguide in the bundle, the entrance angle and energy were calculated as shown in Fig. 17. The X=Y plane is aligned Fig. 14. (Color online) Right: bar target as seen directly by the thermal camera. Left: image transmitted through the HGW bundle. Fig. 16. (Color online) Thermal image of a tungsten wire and a lead rod heated by an electric current. The image was transmitted by a HGW fiber bundle (left) 0:5 mm lead rod at 190 C (right) hot wire at 230 C. 1 September 2010 / Vol. 49, No. 25 / APPLIED OPTICS 4707

9 qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi L ¼ Z 2 1 þ P2 : ð6þ Fig. 17. (Color online) Calculation of the entrance angle and light energy for one waveguide located at point 2 in the fiber bundle from a single light source located at point 1. with the fiber bundle end facing the target image. Given that a point light source is located at ½x 1 ; y 1 ; z 1 Š above the proximal end of the fiber bundle (point 1 in Fig. 17) and a certain waveguide in the fiber bundle located at fx 2 ; y 2 ; 0g (point 2 in Fig. 17), it is simple to calculate the traveling distance and the entrance angle to the waveguide. Calculating the distance will give us the relative energy entering the waveguide (as explained in Subsection_3.B) and together with the entrance angle, we can obtain the output energy of each waveguide in the fiber bundle due to that single light source. Assuming L r (L is the distance between the light source and r is the single waveguide diameter), we assumed that all the energy entering the waveguide enters at the same angle. The distance on the X=Y plane between the light source and a waveguide in the bundle is denoted by P and is obtained by qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi P ¼ jx 1 X 2 j 2 þjy 1 Y 2 j 2 : ð4þ The entrance angle is then given by α ¼ tan 1 P Z 1 : ð5þ The distance from the light source to the single waveguide (L) is given by Fig. 18. (Color online) 2D simulation of the transferred image of the 0:5 mm lead rod through the HGW fiber bundle (left) versus the actual 0:5 mm lead rod image (right). A simulation was done in order to obtain the output energy of each waveguide due to a single source. The same was done for all the pixels in the source image. The total energy at the distal end of a single waveguide in the bundle is the sum of the energy contributions of each pixel in the source image. If we attempted to run this simulation for every pixel in the source image and for every waveguide in the bundle, we would have to run an innumerable amount of simulations, which would take an unreasonable amount of time. Instead, we ran only several simulations for different entrance angles, obtained a normalized graph of the output energy as a function of the angle, and fitted a curve to these results. The fitted curve was then used to obtain the attenuation factor of the waveguide, and the entrance energy was multiplied with the attenuation factor to give the energy of light at the distal end of the fiber (P out ). An example of the results of a 2D simulation is shown in Fig. 18 together with the actual image transferred through the fiber bundle (for reference). In order to estimate the bundle transmission, we summed the energy at the distal end of the bundle and divided it by the total energy at the proximal end of the bundle. Because the output image generation involves summarizing the contribution of each pixel on each waveguide in the bundle, we actually applied the input image 900 times (for every waveguide in the bundle, which consists of 900 waveguides). In order to normalize the output energy, we divided it by 900 multiplied by the input energy: Transmission sum of output pixels ¼ no of bundle waveguides sum of input pixels ¼ 0:059: ð7þ This transmission value is lower than the transmission value we got in the laboratory measurements using the same fiber bundle parameters. This might be, in part, due to the fact that in the transmission measurements, we used the CO 2 laser and measured the transmission at 10:6 μm only. The emitted laser light is a monochromatic, spatially coherent, narrow low-divergence beam and is transmitted in parallel to the fiber axis, while the imaging simulation takes into account the random and diverse nature electromagnetic waves traveling within the hollow waveguide. Nevertheless, the transmission value we got is of the same order of magnitude as the experimental result. 5. Conclusions HGW thermal imaging bundles have been shown to be successful at transmitting infrared radiation from 4708 APPLIED OPTICS / Vol. 49, No. 25 / 1 September 2010

10 a given source and are potentially very useful for endoscopic thermal imaging. The experimental results are encouraging and show an improvement in the resolution and thermal response of the HGW fiber bundles. Current downsides are the low special resolution, due to the larger capillary bore size, and the high loss, owing to the small bore size of the capillaries making up the bundle. This leads to the high temperature of the source at which transmittance is acceptable. Additional decrease of the bundles attenuation is required in order to be able to use this technology for medical applications. Because the losses vary as 1=a 3, where a is the bore radius, in the future, it will be necessary to employ multilayer dielectric coatings instead of a single dielectric film. We expect that it will be necessary to move to newer metal sulfide dielectric coatings rather than the AgI coating, as the metal sulfide thin film materials enable the fabrication of multilayer dielectric coating [16]. Multilayer dielectric coated hollow waveguides can have much lower loss than single layer coated guides, and this will become very important as the bore size of the tubing in the bundle becomes smaller. By using a stack of alternating high and low refractive index dielectric layers, it is theoretically possible to greatly reduce the loss of these HGWs. In addition, it will be necessary to fabricate bundles with even smaller bore sizes for better spatial resolution. Using larger core diameters, HWG can be an immediate solution for some applications. A larger core diameter yields a much better thermal response at the expense of poorer special resolution, which can be acceptable in some applications. In addition, future coherent image bundles need to be flexible, just as they are for visible fiber bundles. This will allow access to remote parts of the body. We intend to make flexible bundles first by the ribbon technique, in which ribbons of small-bore tubing are formed, and these ribbons are stacked to make a coherent array. Those bundles have many clinical applications, as we develop and see. They can be used to measure temperature increase in tumor treatment, in tissue ablation, and in tumor or other lesion temperatures, as well as in photothermal applications [17]. We would like to have the ability to measure a range of temperatures, between room temperature and body regular temperature (36 37 C) up to ablation at 100 C. It will be good to have about 0:1 C in temperature resolution. It will be good to have bundles with an outer diameter of about 1 mm. The flexibility will be helpful to have it inserted in the working channels of endoscopes, so a 5 to 10 cm bending diameter may be sufficient. The authors thank the U.S. Israel Binational Foundation for their support of this research through grant References 1. J. 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