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The Fine Scale Optical Range Peter Mack Grubb Texas A&M University – Computer Engineering Student Dr. Tom Pollock Texas A&M University – Aerospace Engineering Professor Dr. Chip Hill Space Engineering Research Center - Director Abstract The Fine Scale Optical Range (FiScOR) has been designed and assembled to study the efficacy of on-orbit debris characterization using small space-based cameras. Physically, this facility permits imaging of small, one to two centimeter models of simple or complex shapes from a distance sufficiently great to produce image sizes of about one pixel. The objects are designed in 3D CAD and produced in plastic by 3D printing and CNC milling. They are then surfaced in such a way as to approximate a white, completely diffuse surface. Details, such as imperfections in the surfacing of the objects, are achieved to dimensions as fine as 200 micrometers. Mechanisms are provided to rotate and translate the object. Illumination sources approximating the solar spectrum are used. Light curves are recorded using CCD or CMOS cameras which may be cooled or at ambient temperature. For the study reported herein, a few simple objects (cubes, cylinders, etc.) were imaged using a high frame rate color (Bayer mask) camera. Data obtained were compared with Phong models, and to a limited extent, with night sky images obtained using the 0.8m telescope near Stephenville, TX and smaller instruments located near College Station, TX. Introduction Currently there is great concern in the Aerospace and Defense communities about the proliferation of orbital debris[1]. A very small piece of debris in orbit can completely destroy a multi-million dollar satellite just by being in the wrong place at the wrong time[2]. When this was confined to large objects that were known to be in orbit, it was of limited concern, as it was very simple to map and calculate the orbits for these objects. However, with the growth of anti-satellite weaponry[3][4] and the general disrepair of satellites that have been in orbit for many years, a phenomenon known as “debris fields” has begun to be a problem. While the general orbit of the field as a whole can be modeled, there are two challenges that make these fields of great concern[5]. Firstly, over time they expand from the event that originally caused the debris field to form. This will allow objects to drop into higher or lower orbits that have large differences in location very quickly. Secondly, there is no established method for tracking these objects. To establish an accurate orbit for an object, observation across multiple orbits is necessary. However, accurately identifying a single dot in a changing field of dots is highly problematic. To this end, a method for identifying objects in some consistent way is desired One method for identifying objects is by determining their physical properties. Physical properties such as material composition and object shape rarely change from one orbit to the next. Thus, if an object can be quickly identified by its physical properties from one orbit to the next, it becomes distinguishable. However, before methods of quick physical property determination can be developed, accurate light curves for known objects must first be collected. Light curves of known objects have multiple sources. One such source is ground based astronomy of known objects. This provides very accurate data, but is limited by the nature of objects in orbit. Additionally, it is somewhat impractical as quickly imaging a wide variety of objects needed for algorithm development is highly expensive. Thus, a method of accurately imaging known objects in an orbit like scenario is needed in order to create accurate light curves for supporting modeling efforts. To this end, the research team has created The Fine Scale Optical Range. Using small models at the end of a mirror pathway 46 meters in length, we have created a method of accurately imaging these objects at sizes analogous to what would be seen in an orbital scenario. This allows imaging of many models in a short amount of time. These models can be fairly simple or highly complex shapes, with dimensional resolution down to 200 micrometers. These shapes are then translated and/or rotated with continuous imaging by high speed digital cameras to generate a series of images which can be reduced to a light curve. These light curves can be favorably compared to Phong models [6] using various methods. The one used in this paper is to take the raw data of a Phong model and its corresponding data from FiScOR and calculate the normalized cross correlation coefficient. These methods can provide a baseline to compare the efficacy of FiScOR as a method for gathering real data. This project was inspired by and is a continuation of star tracking activities currently taking place at the Space Engineering Research Center (SERC). The images of real objects can be scaled and inserted to scenario imagery generated by the Virtual Sky Imager (VSI) software developed by Dr. Mortari[7]. Because of its origins in star tracking, FiScOR focuses on small cameras, such as what can be found in this application. By comparing the results against Phong, we intend to show both that the FiScOR model is accurate in general and that it picks up key features not found in the Phong model making it or some other analogue a necessity for studying small debris and space objects. Additionally, we intend to show that collecting color data allows us to study subtleties in the data which are otherwise invisible. Methods The fundamental assumption that makes the FiScOR possible is the idea that compared to a wavelength of light, both the small 1-2 cm models and a full size object are extremely large. Thus, from the perspective of the light gathered, the size of the actual object is somewhat unimportant. All that matters is the scaling and composition of the light. Based off of this assumption, FiScOR minimizes the amount of space that it takes to get an accurate light curve. The system consists of three parts: The model and illumination, the mirror pathway, and the camera. The overall system is pictured in Fig.1. Note that the light source is not explicitly pictured. It may be placed in any location on the table where it does not interfere with one of the image pathways. However, it is recommended that there be some sort of baffle for the light source to prevent unintended reflections. Fig.1. The overall layout of FiScOR is quite compact. The entire room needed for it is only 5 meters by 4 meters, and the distance from mirror 1 to mirror 2 2 is about 5 meters. The model is illuminated by a quartz halogen light source with a fiber optic feed designed to mimic solar lighting. As a part of setup, the light source was measured using a USB Stellar-Net® spectrophotometer. The spectrum of the light source is shown in Fig. 2. 160.00 Intensity (μW/cm²/Δλ) 140.00 120.00 100.00 80.00 60.00 40.00 20.00 0.00 200 300 400 500 600 700 800 900 1000 λ (nm) Fig. 2. Spectrum of Light Source. This source emits more light in the near infrared than is found in sunlight, even with an IR blocking filter in place. Fig. 3. Note the back half of the object is not illuminated. This light source has a baffle and IR filter to limit unintentional reflections off other lab apparatus and excess photon count respectively. The light source is pointed at the model as pictured in Figure 3, which rests on stalk mounted on an electric motor, the combined height of which is 10cm. The model itself can be mounted at any axis of rotation, and should be approximately 1-2 cm in diameter. Opposite the light source on the far side of the model is a second light baffle, once again for the purpose of preventing unintended reflections. The models are built using both 3D Fig. 4. The models for this paper printers [8][9] and CnC machines. They can be as simple as a cube or flat sheet have been painted white with a like the models in Fig. 4, and as complex as a scale model of a known orbital black stalk supporting them. object such as the ISS or Hubble Telescope. These models can be covered in various real materials, so that the table can be used to measure and compare light curve data from not just shape, but also physical properties. Additionally, the models can be spray painted for various effects. Wire models for the objects used in this paper along with their designations can be found in Fig. 5. Cube 1 Cube 2 Cube 3 Cube 4 Octagon Fig. 5. The cubes each rotate about a different axis, providing various different light curves for study. The Octagon provides a contrasting shape type to the similarity of the cubes. The second part of the system is the mirror path. The motivation behind the folded mirror path is minimization of floor space. For the models to be the appropriate size in the camera Field of View (FOV), the model needs a light path approximately 46 meters long. Finding such a space in a lab building is often impractical. Thus, via a mirror assembly the entire path is compressed into a room 5 by 4 meters. This reduces costs and makes running FiScOR more feasible. This portion of the system is laid out in Fig. 1. It consists of 13 mirrors (numbers 2-14 in Fig. 1), one of which is pictured in Fig. 6, each 35 by 26mm, a 30.5 by 77 mm mirror (number 1 in Fig. 1) at the beginning, and a 84 by 121 mm mirror (number 15 in Fig. 1) at the end attached to a motorized apparatus. Each of the mirrors has an apodizing mask to eliminate diffraction edges[10][11][12]. The end result of this is a path way 46 meters long. For this implementation, 1/10 lambda first surface mirrors with enhanced coatings were used, which gives us a very flat surface with minimal light Fig. 6. The back of the mirror has the screws that allow for fine adjustment both vertically and horizontally. loss. The motorized apparatus in the final mirror serves to simulate translational motion on the part of the model. This apparatus is essentially an eccentric cam system, which is driven by an electric motor. By running the motor, the final mirror is titled in a periodic fashion. This allows for simulating translational velocity of the model. The final component of FiScOR is the camera itself. Virtually any camera may be used, but accurate light curve determination requires a large number of images per revolution. If a high speed camera is unavailable, this can be achieved via electric motors capable of slow turn rates. In the case of FiScOR, the Silicone Imaging® SI640-HFRGB pictured in Fig. 7 was used. This selected because it is a high frame rate color camera which uses a Bayer mask[13] and a high speed Camera Link interface. An EPIX PIXCI® EB1 interface card and the EPIX XCAP® software were used for the purposes of frame grabbing. This allowed for captures on the order of 400 frames per revolution of the models in full color. The system is flexible as to lens Fig. 7. The Camera is mounted on an type, but it was found that large aperture lenses were needed for the articulated head with 3 degrees of freedom. object to be visible. The lens used in this implementation of FiScOR was a Canon® 85mm F1.2 lens. The reason for the color camera is that a large part of the motivation behind FiScOR is to move beyond gray scale imagery for object identification. Some materials such as Solar Cells or the Gold Multi-Layer Insulation (MLI) used in satellites have very distinctive color signatures. A monochrome camera will often lose details such as this, rendering objects indistinguishable. By using a color camera, objects of the same shape with different real material coverings can be imaged, and their R, G and B data compared separately. This provides a potential avenue for material determination that has not been fully explored. In addition to the data gathered using FiScOR, Earth based observations were done using the 0.8m telescope at Tarlton State University. These images were used as references to provide a baseline for the accuracy of FiScOR. The other type of data that was gathered to compare FiScOR against was Phong models. These models were built in DesignCAD 3D Max versions 18 and 19, and then illuminated using the Phong model built into the software as shown in Fig. 8. The models were then rotated in 2 degree increments, with the screen captured at each step. The light source can then be moved to a new location, and the image gathering repeated. This process was scripted using the open source tools AutoHotkey and Greenshot. Results Fig. 8. DesignCAD 3D Max Allows for accurate 3D model generation and lighting. Once the data was gathered from both FiSCoR and the Phong models, it was analyzed using Matlab. This analysis took two forms: normalized cross correlation constants, and matched graphs. For the cross correlation constants, the Matlab function xcorr() was used. However, for cross correlation to have any meaning, the time step in the data must be equal. Thus, prior to running xcorr, the data was up-sampled using the Matlab function interpolate() until both the Phong model data and the FiScOR data had the same number of samples. Additionally, the data sets were normalized by dividing each element by the integral of the data set, giving an area under the curve of 1 in the resulting set. The results from this are recorded in Tables 1 through 4. Table 1. 10 deg Horizontal, 16.5 deg Altitude Table 2. 45 deg Horizontal, 16.5 deg Altitude Red Green Blue White Cube 1 0.999981 0.999948 0.999947 0.999972 0.999979 Cube 2 0.999982 0.999938 0.99993 0.999979 0.999787 0.999893 Cube 3 0.999979 0.999937 0.999935 0.999971 0.999954 0.999927 0.999963 Cube 4 0.999971 0.999883 0.999848 0.999913 0.999906 0.999859 0.999908 Octagon 0.999967 0.999881 0.999826 0.999904 Red Green Blue White Cube 1 0.999976 0.999912 0.999891 0.99995 Cube 2 0.999979 0.999931 0.999907 Cube 3 0.999969 0.999828 Cube 4 0.999979 Octagon 0.999942 Table 3. 90 deg Horizontal, 16.5 deg Altitude Table 4. 135 deg Horizontal, 16.5 deg Altitude Cube 1 Cube 2 Red 0.999992 0.999989 Green 0.999989 0.999975 Blue 0.999949 0.999974 White 0.999991 0.99999 Cube 1 Cube 2 Red 0.999993 0.999984 Green 0.99999 0.999976 Blue 0.999987 0.999968 White 0.999991 0.99998 Cube 3 Cube 4 0.999991 0.999982 0.999975 0.999981 0.99996 0.999974 0.999983 0.999986 Cube 3 Cube 4 0.999991 0.999976 0.999971 0.999974 0.999959 0.99997 0.999977 0.999976 Octagon 0.999991 0.999964 0.999971 0.999982 Octagon 0.999996 0.999996 0.999993 0.999997 The other method used for comparing the data was visual. A Matlab script was created to graph each color against its corresponding Phong model. First, the script took the interpolated data that was input to xcorr() and found the difference in their relative magnitudes. Based on this factor, the Phong model was scaled to match the Real data. Then, the means of the two distributions were aligned. This allows the data to be graphically compared, giving a more detailed picture as to what the data means. To show the periodic nature of the data, two full revolutions are pictured in the graphs below. The graphs for Cube 2 and the Octagon are included in Fig.’s 9-16. Fig. 12. Fig. 9. Cube 2 -10 deg Horizontal, 16.5 deg Altitude Fig. 10. Cube 2 -45 deg Horizontal, 16.5 deg Altitude Fig. 11. Cube 2 - 90 deg Horizontal, 16.5 deg Altitude Fig. 12. Cube 2 -135 deg Horizontal, 16.5 deg Altitude Fig. 13. Octagon -10 deg Horizontal, 16.5 deg Altitude Fig. 14. Octagon - 45 deg Horizontal, 16.5 deg Altitude Fig. 15. Octagon - 90 deg Horizontal, 16.5 deg Altitude Fig. 16. Octagon -135 deg Horizontal, 16.5 deg Altitude Discussion The cross correlation constants were quite high, virtually indistinguishable from a perfect 1 in many cases. This was initially a cause for concern, as this does not mesh with the disparities apparent in the graphs. For example, in Fig.17 there are a series of peaks in the Phong data where the image data actually dips. However, the White light in this example has a cross correlation coefficient of 0.999908. This seems counter intuitive, but it is important to remember what cross correlation measures. Because cross correlation measures the relative curves against each other at every point, it represents a best case measure of how alike the curves are if their magnitudes and ranges are similar. Thus, this number represents a best case of how similar the light curves are. Taking this into account, the two sets of light curves are remarkably similar. Based on this data, we were able to actively fine tune the Phong materials to get “measured Phong parameters” for the objects used. From this set of results alone, we can see that FiScOR is accurately measuring object illumination in aggregate. However, if the two sets of data were exactly identical, there would be no sense in using FiScOR. While the data sets are on the order of 99% similar, the graph comparisons show that there are individual features in real data that are completely missing from Phong. For example, in Fig. 12, the peaks in Phong are actually in better phase with the dips of the real data, especially for the red spectra. This is because Phong does not account for the diffuse reflection of specular light. When the light source is at 10 degrees, the diffuse reflected intensity is great enough that this fraction is insignificant. However, when the light source is at 135 degrees, this forms a significant portion of the light and in the case of the red light, is actually more significant than the diffuse which the Phong model sees. These graphs show that as the light source moves around towards the back of the object, the Phong model becomes less indicative of reality. Thus to accurately measure all the light angles associated with small objects in orbit, something like FiScOR is needed. While the aggregate data is accurate from Phong, the specific features which would be useful in object identification are not necessarily perfectly predicted by the Phong model. Another point of interest in the graphs is the differences between the different color spectra of light. While the general waveform was quite similar, there were features in each color spectra not present in the others. For example, in Fig. 13, the maximum for green and blue is in a different peak. If the object is white, the Phong model assumes that its reflection is identical in all 3 spectra. This is obviously not true from the data above, thus necessitating the use of a system like FiScOR. Note that the magnitude of the red light captured is low across all the graphs. This is due to the specific brand of white paint used. Most white paints are not true white, as was clearly true in our case. Conclusion The FiScOR system performed extremely well. When the data was compared in aggregate with Phong models via the cross correlation coefficient, the results were found to be quite close. However, the FiScOR graphs were found to have features not present in the Phong models. Phong’s inability to model the diffuse reflection of spectral light became quite significant in situations with dim objects. Our process also found that results differ between the colors, even for white objects. These subtleties could prove to be quite important when trying to identify objects from the light curves. However, if the images are done in greyscale, these subtleties are lost. The next step with this project is to do further work with FiSCoR and alternative material types. The color data will probably be more significant when different material types such as MLI or solar panels are imaged. Thus, the next step is to investigate these differences. A further evolution of this paper involving additionally materials will be presented at the Advanced Maui Optical and Space Surveillance Technologies Conference by the same authors. Acknowledgements None of this project would have been possible without the lab facilities and equipment provided by the Space Engineering Research Center. In addition, thanks is due to the Research Opportunities for Engineers Scholarship program, which funded one of the primary authors. Finally, a special thank you is due to Dr. Christian Bruccoleri for Matlab Coding and general mentorship throughout the project. References 1. David S. F. Portree, Joseph P. Loftus, Jr., Orbital Debris: A Chronology. NASA publication NASA/TP-1999208856, 1999. 2. V.M. Smirnov et al, "Study of Micrometeoroid and Orbital Debris Effects on the Solar Panels Retrieved from the Space Station 'MIR'", Space Debris, Volume 2 Number 1 (March, 2000), pp. 1 – 7. doi:10.1023/A:1015607813420 3. William J. Broad and David E. Sanger. “Flexing Muscle, China Destroys Satellite in Test.” New York Times. January 19th, 2007. <http://www.nytimes.com/2007/01/19/world/asia/19china.html?_r=1&pagewanted=all> 4. "Debris from explosion of Chinese rocket detected by University of Chicago satellite instrument", University of Chicago press release, 10 August 2000. 5. Antony Milne, Sky Static: The Space Debris Crisis, Greenwood Publishing Group, 2002, ISBN 0-275-97749-8, p. 86. 6. B. T. 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