Pseudo-color enhanced x-ray fluorescence imaging of the Archimedes Palimpsest

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1 Invited Paper Pseudo-color enhanced x-ray fluorescence imaging of the Archimedes Palimpsest Uwe Bergmann a, Keith T. Knox b a SLAC National Accelerator Laboratory, 2575 Sand Hill Road, Menlo Park, CA, USA b Boeing LTS, 535 Lipoa Pwky., Suite 200, Kihei, HI USA ABSTRACT A combination of x-ray fluorescence and image processing has been shown to recover text characters written in iron gall ink on parchment, even when obscured by gold paint. Several leaves of the Archimedes Palimpsest were imaged using rapid-scan, x-ray fluorescence imaging performed at the Stanford Synchrotron Radiation Lightsource of the SLAC National Accelerator Laboratory. A simple linear show-through model is shown to successfully separate different layers of text in the x-ray images, making the text easier to read by the scholars. Keywords: image processing, x-ray fluorescence, enhancement, pseudo-color 1. INTRODUCTION The Archimedes Palimpsest is a thousand-year old manuscript that contains seven treatises of the Greek mathematician, Archimedes. Eight hundred years ago, the writings were erased and overwritten with the Euchologion text of a Christian prayer book. In 1998, the manuscript was purchased at auction by a private collector. Over the last ten years, a team of researchers has devoted a significant effort to recover the erased writing of Archimedes. The history of the project was recorded in a recent book by Review Netz and William Noel [1]. The current status of the project can be found on Multispectral methods using visible and ultraviolet light have been used to read most of the writings, but some leaves could not be read this way. A few of them were either too damaged or had been erased a second time in the Twentieth Century and painted over with forged icons. Using a rapid-scan, x-ray fluorescence technique at the Stanford Synchrotron Radiation Lightsource (SSRL), it was possible to image these leaves, by detecting faint traces of the iron in the ancient iron gall ink, even in regions that were covered with gold paint. The difficulty with x-rays is that they also go through parchment. That means that the x-ray images contain characters from both sides of the parchment. Sophisticated image processing is required to separate the different layers of text to enable the scholars to read the obscured writings. 2. X-RAY FLUORESCENCE (XRF) IMAGING X-ray fluorescence (XRF) has been used for many years for quantitative elemental analysis of a large range of systems including very dilute and thin materials. In XRF analyses x-rays are used to knock out the inner-shell electrons from the elements of interest. As a result, a spectrum of characteristic XRF lines is emitted, each line corresponding to the respective transitions from the various elements in the sample, such as Kα, Kβ, Lα etc. The intensities of these lines are recorded with an energy sensitive detector. With proper calibration, the quantitative elemental composition of the sample can be determined. XRF analyses are often used to detect and quantify trace elements, and as such it is one of the most sensitive non-destructive techniques, in particular for elements that emit x-rays in the harder x-ray regime (> 3 kev). The XRF spectrum taken on the Archimedes Palimpsest during an imaging scan is shown in Figure 1. For this scan, the x-ray beam energy was set to 15 kev. The spectrum was recorded with a Si drift detector and the XRF line widths are given by the detector resolution. Most of the depicted lines correspond to the Kα emissions, some other XRF lines are labeled in the figure. Document Recognition and Retrieval XVI, edited by Kathrin Berkner, Laurence Likforman-Sulem, Proc. of SPIE-IS&T Electronic Imaging, SPIE Vol. 7247, SPIE-IS&T CCC code: X/09/$18 doi: / SPIE-IS&T/ Vol

2 In addition to the fact that x-rays can penetrate visibly opaque matter, it is the element specificity and its excellent sensitivity that makes XRF a powerful tool for imaging. For objects with low concentration, or a very thin layer of material of a particular element, XRF images produce a better contrast as compared to a conventional x-ray transmission image (radiograph). For that reason, XRF was chosen to image the hidden Archimedes writings, with particular focus on the iron in the remaining parts of the partly erased and covered ink. Unlike a radiograph, an XRF image cannot be produced with a large area exposure, because the XRF signal is emitted in essentially all directions, and hence the origin of the signal is lost. In order to obtain an XRF image, the object has to be raster scanned across a small x-ray beam, and the XRF signal is recorded for each interaction point with the beam. The x-ray beam size determines the spatial resolution of the image, and a sufficient XRF signal per pixel is needed in order to obtain a good image quality. Ca Fe P S Cl Ar K Ca Kβ Ba Lα Fe Kβ Cu Kβ XRF Energy [ev] Fig. 1. XRF spectrum of a parchment leaf of the Archimedes Palimpsest taken during an imaging scan across the writings. All XRF lines correspond to Kα transitions unless indicated otherwise. The argon XRF peak originates from the air around the parchment. Excitation energy for this spectrum is 15 kev. Mn Cu Zn In order to image a page of the Archimedes Palimpsest at ~ 40 µm resolution (corresponding to 600 dpi), approximately 12 million measurements (pixels) are required. To accomplish this in a reasonable time, each measurement has to be taken very rapidly. This in turn requires a very powerful x-ray beam, and a fast scan, detector, and readout system. Synchrotron radiation sources are the only facilities that provide such powerful and stable x-ray beams. In particular, at insertion device beam lines on a third generation synchrotron facility, such as the SSRL, a very intense, highly collimated, energy tunable and polarized x-ray beam can be produced. Over the last two decades, researchers at synchrotron facilities have been focusing most of their efforts in XRF imaging on improving the spatial resolution to image ultra-small structures. A different direction was required for the XRF imaging of the Archimedes Palimpsest [2]. Rather than pushing for a higher spatial resolution, it was critical to enhance the imaging speed. Very recently, low resolution XRF imaging also has been used by another group to visualize a hidden painting by Vincent van Gogh. In their experimental arrangement, it required 2 days to image a 17.5 cm by 17.5 cm region of the painting using a dwell time of 2 sec/pixel [3]. SPIE-IS&T/ Vol

3 3. EXPERIMENTAL SETUP XRF imaging was performed at wiggler beam lines 6-2 at the 3 GeV SPEAR3 ring at SSRL (Fig. 2). The beam line was operated in standard configuration with a collimating total reflection mirror (M 0 ) upstream of a Si (111) monochromator, and a doubly focusing total reflection mirror (M 1 ) downstream. The beam was further passed through a motorized collimator slit and focused onto a 50 µm diameter tantalum pinhole placed close to the parchment. Since the sample was mounted at a 45 o angle to the incident beam, the 100 µm thick pinhole was tilted such that the horizontal beam size was reduced to 50/ 2 = 35 µm, which in turn results in a 50 µm footprint on the sample. Wiggler (54 pole, 1T) slit 1 slit 2 M 0 M 1 collimator slit pinhole Si mono 13.86m 18.80m 25.00m Fig. 2. Schematic outline of SSRL beam line 6-2. X-rays created in the 54 pole wiggler are collimated by total-reflecting mirror (M 0 ) onto Si (111) monochromator and focused by doubly focusing total-reflecting mirror (M1) onto a collimator slit. The tantalum pinhole slit (100 µm thickness, 50 µm diameter) is tilted horizontally to produce a 50 * 35 µm 2 highly collimated (pencil) beam impinging onto the parchment. Two detectors were used to record the XRF signal (see Fig 3). For the front side, a photon counting 13 element germanium detector system (Canberra) with Gaussian shaping amplifiers employing µsec shaping times, plus single channel analyzers was used. For each element, the electronic (single channel analyzer) windows were set to capture the fluorescent photons from the Kα emission lines. The signals of all 13 detector elements within the window of each chemical element were added with a fan-in unit (LeCroy model 127FL) and the sum signals were fed into the readout system. A second photon counting single element silicon drift detector (Vortex) was used to record the XRF signal from the back side of the leaf. It also used Gaussian shaping amplifiers with µsec shaping times combined with single channel analyzers. Both detectors were placed at a 90 o angle to the horizontally polarized x-ray beam in order to minimize the unwanted scattering signal. The parchment leaves were mounted on a computerized X-Y translational stage and rapid scans were performed by continuously translating the sample horizontally across the beam. At the end of each line a vertical step (40 µm/step) was performed, and the horizontal scan direction was reversed. This bidirectional scanning scheme avoids dead time during rewinding, but requires exact synchronization of motor speed and readout time in order to avoid misalignment of subsequent lines in the image. XRF data were collected at a rate corresponding to a travel distance of 40 µm per readout. During the first run, a readout system used custom built real-time software coupled with standard beam line hardware to provide deterministic data acquisition. The system had adjustable count times in units of 10 milliseconds (ms) plus ~2.8 ms overhead per readout. To further increase scanning speed, new hardware was developed to scan without measurable dead-time (overhead) between data points. The concept of the system is to collect an entire line of data into a local memory area, and transfer it to the control computer at the end of each line. The hardware uses a programmable timer to precisely set the data measurement time and the internal data buffers to decouple the measurement timing from the data transfer process. Electronics are implemented in a Xilinx Virtex-4 Field Programmable Gate Array featuring an embedded PowerPC microprocessor. The embedded system is built using a Xilinx Embedded Development Kit software. The peripheral SPIE-IS&T/ Vol

4 device contains a 32-bit timer with 10 ns resolution, sixteen 32-bit counters with maximum count rate of 10 MHz, data point counter and trigger and interrupt logic. The peripheral device is implemented in Very High Speed Integrated Circuit Hardware Description Language. At the end of each measurement, additional counter logic stores the measurement results in the buffer register and starts the next measurement with no delay. An interrupt is generated after each measurement, and the microcontroller moves data from registers to large (8 MB) secondary buffers. To keep the amount of data at a manageable level only integrated regions of interest (ROIs) were recorded for every readout (rather than the whole XRF spectra). ROIs are set to the energy range of an XRF line as recorded in the detector. For example, to record the Fe Kα line the ROI is 6400±200 ev (see Fig. 1). A total of 16 channels were registered including two beam intensity monitors, the scattering signal and six or seven ROIs from each detector. A lower priority software process transfers the buffered data to the computer, so any delays at the communication link or host computer do not affect the data acquisition timing. In addition to programmable measurement timing and input/output polarity, the electronics can convert data to 16-bit values and send measurement results only from specified counters to reduce the amount of transferred data. Using this system, we were able to increase the scanning speed by a factor of four to ~ 3 ms per pixel. Archimedes Palimpsest XRF Imaging Layout Viewed from Above - continuous x-scans - steps in z-direction 5Oro pinhole x I Fig. 3. The experimental arrangement of the x-ray detectors. Left: The parchment was mounted at a 45 degree angle to the incoming x-ray beam. The pinhole close to the palimpsest and an upstream collimating slit (not shown) ensure the well defined beam at the sample. Two detectors captured the x-ray fluorescence that was emitted at 90 degrees from the beam. One detector captured the fluorescence from the front of the parchment and the other from the back. A third detector was aligned with the beam and was used to monitor the beam strength over time. Right: front view showing the schematics of the scanning procedure. The x-range for most scans was smaller than the width of the parchment and at the end of each x line, a pneumatic shutter is inserted to protect the parchment. 4. EXPERIMENTAL RESULTS So far, there have been three x-ray imaging sessions conducted at SLAC, one in 2005 and two in Several difficult leaves were imaged using the specially designed x-ray imaging experimental setup. Leaves were chosen that were very difficult to image using optical methods. There were three different types of imaging problems that were considered. The first was very faint text. It was hoped that faint traces of iron were still in the parchment and would make the writing visible. Unfortunately, this turned out not to be the case. This experimental imaging setup had very little success with very faint text. The second type of problem considered was very degraded parchment. The outer leaves of the book, such as folio 1, had suffered significant environmental damage. Although not discussed in this paper, the x-ray experiments with folio 1 were very successful. This was very fortunate, since this folio contained the inscription by the scribe that created the palimpsest. From the images of folio 1, the scholars were able to determine that the scribe s name was Johannes Myronas and that he completed the prayer book on the 14 th of April in the year The third type of damaged leaf considered was the painted icon. Four pages of the prayer book were cut from the book, erased and forged icons were painted on the leaves. This was done sometime in the first half of the twentieth century, SPIE-IS&T/ Vol

5 perhaps in an attempt to make the book more valuable on the art market. An example of one of the leaves with a painted icon is shown in Figure 4. t.. 1 ' $"_ TT S Fig. 4. The left side of this figure shows the visible image of folio 81 recto, while the right side shows the flip side, 81 verso. Both leaves had been erased and the 81 recto side was covered with a painted forgery of a Byzantine icon. Unfortunately, the paint completely obscures any optical detection of the characters underneath. The paint stops both the ultraviolet and the visible illumination. There are places within the icons were the paint has flaked away revealing some characters, or parts of characters, but most of the text is obscured. The largest area is obscured by the gold paint in the background of the icon. Fortunately, this paint does not contain iron and the text underneath it is visible in the x-ray fluorescence image. The most significant problem with this area is that four layers of text are mixed together, two from each side of the leaf. It is the separation of these layers that will be addressed in the rest of the paper. 4.1 Optical imaging versus x-ray fluorescence imaging of the Archimedes Palimpsest There have been several imaging sessions of the Archimedes Palimpsest over the last 10 years. The most recent was in August At that time, the complete manuscript, all 177 leaves, were optically imaged in 11 bands, from the ultraviolet, through the visible and into the near infrared. Most of the erased text was recovered using ultraviolet and visible illumination and a pseudo-color processing technique [4] to enhance the contrast of the erased text. A few leaves were very difficult to image optically and these became prime candidates for x-ray imaging. The optical image of one of the painted icons, folio 81 recto, is shown in Figure 4. The reverse side of the leaf, folio 81 verso, is shown on the right side of Figure 4. The paint of the icon stops any optical illumination, ultraviolet through near infrared, and makes imaging the text underneath the paint next to impossible. The verso side was erased, but it was not painted, so that erased text is recoverable by optical means. SPIE-IS&T/ Vol

6 To recover the erased text optically, an ultraviolet image of the leaf is combined with a visible image (typical in the red) of the same leaf. The two images are taken sequentially, without moving the leaf in between exposures. This ensures that the two images are in perfect registration. Under ultraviolet illumination, the parchment fluoresces in the visible, thereby increasing the contrast of both the erased text and the overwriting. Both these images are contrast adjusted to equalize the variation of contrast across the leaf. This allows equal values of the two images to be compared. A pseudo-color image is created by putting the contrast-adjusted visible image in the red separation and the contrast-adjusted ultraviolet image in the green and blue separations. The key is that the erased Archimedes text is reddish in color, so it disappears under red light, while the ultraviolet illumination increases the contrast of the erased text, making it dark. As a result, the erased text turns red in the pseudo-color image. The Euchologion overwriting, on the other hand, is equally visible in both images, so it appears as a neutral gray in the pseudo-color image. The pseudo-color images of folio 81 recto and verso are shown below in Figure 5. The erased text, on the erased folio 81 verso, turns bright red and stands out on the page. There are two directions of text visible in this image, one vertical (the Archimedes text in this orientation) and one horizontal, the Euchologion text. Very little of any erased text appears on folio 81 recto, because the paint obscures the writing. Fig. 5. Under ultraviolet illumination, the erased writings fluoresce in the visible bands. The erased text is emphasized using a pseudo-color technique that combines together the visible and ultraviolet images to turn the erased writings red. Unfortunately, the paint blocks the ultraviolet and visible illuminations, so the text under the painted icon is not legible. The x-ray fluorescence images show a completely different picture. The two images, from the front and back detectors, are shown in Figure 6. There are several things to note about these images. The first is that the two images are in perfect register with each other. Since only one pixel is illuminated at one instant, the counts acquired by each detector correspond exactly to the same pixel location on the parchment. This allows the two images to be compared to each other without any spatial adjustments. SPIE-IS&T/ Vol

7 The second point is that these two images, one of the front side and the other of the back side, show details from both sides. Since each side of the leaf has two layers of writing, the erased Archimedes text and the existing Euchologion text, the x-ray images have four layers of writing visible. This makes the images much more complicated to interpret than the optical images, which have only two layers of writing each. The third point of interest is that the icon image in Figure 6 is reversed from the icon images in Figures 4 and 5. The scan was made with the recto side of the parchment (the side with the icon) facing away from the x-ray beam. As a result, the icon is seen through the parchment and is reversed from the optical image taken from the recto side of the leaf. The text from the recto side is also reversed in these x-ray images. The fourth and last point is that the texts in the two images have different strengths. It appears that the text on the verso side (facing the x-ray beam and the front detector) has proportionally higher counts on the front detector than it does on the back detector. To reach the back detector, the fluorescence has to travel through the parchment. Its strength on the back detector is apparently decreases by the travel through the parchment. This will prove to be a valuable characteristic as we try to separate the texts from the two sides. Fig. 6. These two images show the amount of iron detected by x-ray fluorescence from the front (left) and back (right) detectors. The verso side of the leaf was facing the x-ray beam, so the icon is reversed horizontally from Figures 4 and 5. Note that since the x-rays pass through the parchment, 4 layers of text, 2 from each side, appear in both images. 4.2 Pseudo-color The pseudo-color technique, which emphasized the erased text by turning it red, can also be used with the x-ray images to differentiate between the text from the two sides of the leaf. In the optical image, the text disappeared in only one image. In the x-ray images, neither text disappears, but the two texts brighten and darken in the opposite directions. Figure 7 shows blowups from the images in Figure 6. The images have also been rotated clockwise 90 degrees to put the Archimedes text in a horizontal left-to-right reading orientation. Both images have been locally contrast adjusted, so that brighter characters in both images have approximately the same value, as do the dimmer characters. SPIE-IS&T/ Vol

8 I, Fig. 7. Blowups of the images in Figure 6. Note that these images have been rotated 90 degree clockwise. On the left side of both images, a vertical column of jumbled characters is visible, but the relative strengths differ in the two images. These two images were combined in a pseudo-color image, which is shown in Figure 8. One image from the front detector was put in the blue separation of the pseudo-color image, while the back detector image was put in the other two color separations. Since the front detector shows the text on folio 81 verso more brightly, that text appears blue, while the text from the other side is yellow. The colors obviously will not show in the black and white printed copy. Fig. 8. A pseudo-color combination of the two images from Figure 7. The text from 81 recto is yellow, while the text from 81 verso is blue. In the black and white printed version of this page, this distinction will not be apparent. This can best be seen in the vertical column on the left half of each image. In this column, there are several horizontal lines of text. Each text line contains a jumble of characters from horizontal and vertical writing from both sides of the parchment. In the pseudo-color image, however, two of those character sets are yellow and the other two are blue. This color differentiation helps the scholar to separate the two writings and read them independently. The scholars have read the pseudo-color x-ray images and although the pseudo-color does help them distinguish the text from the two sides, their feedback is that the text is still difficult to read. As a result, we have continued our efforts to SPIE-IS&T/ Vol

9 develop a technique that completely separates the texts from the two sides of the parchment. Our most recent effort is the subject of the next section. 4.3 Linear show-through model The difference between the texts on the two sides of the parchment is that the text is brighter in the detector to which it is closer. To see if that relationship is linear or non-linear, the values from the two detectors were correlated on the scatter plot shown in Figure 9. In that figure, the value on the back detector, for a given pixel, was plotted against the value on the front detector. The accumulation of points on the plot shows a linear relationship between the two detectors. There are two lines drawn on the figure showing the extremes of the plot. Points along the lower line represent values from text that is only on the front side of the parchment. Points along the upper line represent text that is only on the back side of the parchment. Pixels that contain signal from text on both sides lie somewhere in between the two lines. Fig. 9. A scatter plot comparing the digital counts of the two sensors. The result is an apparent linear relationship. The two lines represent the extremes, i.e. the upper line represents signal that includes only text from the back side (81 recto) and the lower line for text from the front (81 verso). The points in between the lines are mixtures of the two texts. A linear model developed for show-through on paper [5] can be adapted to this relationship. Define the signals from the front and back detectors as F and B, and the true text signals as f and b. The gain of the back detector is assumed to be lower than the gain of the front detector by a factor of G. We also assume that the fluorescence that travels through the parchment is decreased by a factor of T. With these definitions, the signals on the two detectors are given by: F = f + Tb (1) B = Gb + GTf (2) If the gain, G, and degradation, T, factors can be determined, then Equations 1 and 2 can be solved for the true unmixed signals, f and b. The gain and degradation can be determined by considering the two extreme lines on the scatter plot. SPIE-IS&T/ Vol

10 Define the slope of the upper line, that contains only text on the back side, as m b and the slope of the lower line as m f. Also define the detector signals, when there is only text on the back and front, as B b, F b and B f and F f. With these definitions, it is also true that: B f = m f F f (3) When a pixel only contains text from the front, then Equations 1 and 2 become: B b = m b F b (4) F f = f (5) B f = GTf (6) Similarly, when a pixel contains only text from the back side, then Equations 1 and 2 become: F b = Tb (7) B b = Gb (8) Substituting Equations 5 and 6 into Equation 3, and Equations 7 and 8 into Equation 4 yields: m f = GT (9) m b = G T (10) With these equations, the gain and degradation factors can be determined from the slopes of the two extreme lines as: G = m f m b (11) T = m f m b (12) Now that we have G and T in terms of m f and m b, Equations 1 and 2 can be solved for f and b: b = B G TF 1 T 2 ( ) f = F TB G 1 T 2 ( ) (13) (14) For the example shown in Figure 9, the slopes and factors have the following values: m f = m b = 0.18 G = T = 0.60 The detector signals, F and B, are shown in Figure 7, while the separated images, which result from applying Equations 13 and 14, are shown in Figure 10. By comparing the two figures, it is clear that the text, in the vertical column on the left side of the images, has been separated into two parts, each containing some horizontal and some vertical writing. It is also clear that, although the linear assumption separated the text nicely, it is not the complete answer. The icon painting, i.e. the seated figure, the chair, etc., did not completely separate onto one image, as it should have done. Since it was on the back side of the parchment, it should not show up in the front-only image, as it does. That probably means a non-linear model might work better. For example, the non-linear model developed for show-through on paper [6] might be appropriate. Further research is needed to determine the most accurate relationship between the two detectors. SPIE-IS&T/ Vol

11 Fig. 10. The texts from the two sides now separated using equations 13 and 14. The upper image is the text from front side (81 verso) and the lower image is the text from 81 recto. The text visible in the vertical column on the left third of the bottom image is otherwise hidden under the painted icon. SPIE-IS&T/ Vol

12 'I I 4.4 Seeing through the paint 1 Fig. 11. The upper image shows the text from 81 recto. The image has been reversed in the horizontal direction to make the text readable. The detected image was captured reversed, because the icon was turned away from the x-ray beam. The lower two images show the same region in pseudo-color (left) and in visible illumination (right), where the text is covered by the paint. SPIE-IS&T/ Vol

13 To confirm that the text on the bottom half of Figure 10 is from the recto side of the parchment, the recto-only image was reversed horizontally and is shown in Figure 11. Also in that figure are the corresponding optical images. The ultraviolet pseudo-color image on the left and the visible light image on the right. In both of the two optical images, only a few characters are visible in the areas where the paint has peeled away. That means that most of the characters visible in Figure 11 were detected by the x-ray fluorescence through the gold paint on the leaf. 5. CONCLUSIONS X-ray fluorescence was shown to successfully detect the iron in the erased iron gall ink on the thousand-year old parchment manuscript, the Archimedes Palimpsest. The technique was able to see through the gold paint of a forged icon that was obscuring the erased Archimedes text on a few pages. It was also able to see through the parchment, meaning that four layers of text were combined together. By using two detectors, one on each side of the parchment, and a simple linear mixing model, it was possible to separate the text from the two sides of the leaf. ACKNOWLEDGMENTS This work would not have been possible without the generosity and support of the owner of the Archimedes Palimpsest. The authors would also like to acknowledge the significant efforts of William Noel, the Curator of Manuscripts at the Walters Art Museum, Abigail Quandt, the head of Conservation at the Walters, and the other two members of the Archimedes imaging team, Roger Easton, Jr. and William Christens-Barry. Also instrumental in the project, were Michael Toth, who helped manage the project, and Douglas Emery, who helped manage the huge volumes of data. The help of the staff at SSRL, in particular Martin George and Alex Garachtchenko, who were instrumental for developing the rapid-scan setup, is gratefully acknowledged. Portions of this research were carried out at the Stanford Synchrotron Radiation Lightsource, a national user facility operated by Stanford University on behalf of the U.S. Department of Energy, Office of Basic Energy Sciences. The SSRL Structural Molecular Biology Program is supported by the Department of Energy, Office of Biological and Environmental Research and by the National Institutes of Health, National Center for Research Resources, Biomedical Technology Program. The copyright of the manuscript images in this paper is retained by the owner of the Archimedes Palimpsest. REFERENCES [1] [2] [3] [4] [5] [6] Netz, R. and Noel, W., The Archimedes Codex, Da Capo Press, Perseus Book Group, Bergmann, U., Archimedes brought to light, Physics World, p. 29, November Dik, J., et al., Visualization of a Lost Painting by Vincent van Gogh Using Synchrotron Radiation Based X-ray Fluorescence Elemental Mapping, Anal. Chem., 80 (16), , Knox, K. T., "Enhancement of overwritten text in the Archimedes Palimpsest,'' in Computer Image Analysis in the Study of Art (D. G. Stork and J. Coddington), San Jose, California, Proc. SPIE, vol. 6810, Knox, K. T., Show-through correction for two-sided documents, U. S. patent # 5,832,137, 3 November Sharma, G., "Show-through cancellation in scans of duplex printed documents," IEEE Trans. Image Proc., 10(5), pp (2001). SPIE-IS&T/ Vol