Full-Color image reconstruction by holography for 3D X-ray CT

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1 Full-Color image reconstruction by holography for 3D X-ray CT Akifumi Koike, Hisashi Morii, Mitsuhiro Yomori, Yoichiro Neo, Toru Aoki, Hidenori Mimura Shizuoka University, Johoku, Nakaku, Hamamatsu , Japan; ABSTRACT The X-ray 3D CT data were detected by the CdTe semiconductor special detector which can obtain the energy information of X-ray photon, and it is developed by our laboratory. In order to display this complete 3D information with internal data of objects, the multi-color holographic reconstruction system was composed, and the reconstruction of X-ray 3D CT data were examined in this paper. In this system, the electro-holography and the computer generated holography was employed to display holographic images. In this case, we used the liquid crystal display panel as the spatial light modulator for displaying a hologram, and we developed the simulator to calculate a hologram of an X-ray 3D CT input data. Finally, it could represent effectively with three primary colors, and understand easier the internal structure of objects. Keywords: Hologram, Color, 3D, Display, X-ray CT, Energy Discrimination 1. INTRODUCTION The holographic three dimensional (3D) image reconstructions have been attended for the three dimensional display due to that it can display natural complete three dimensional images in an arbitrary space. In the various fields, 3D display is requires for novel information representation system, especially, the medical treatment field and the Non-destructive testing, the baggage check in an airport which use the X-ray penetration and the X-ray Computer Tomography (CT). Because these work requires the high quality and accurately recognition of targets information. However, it is difficult to achieve it in current systems with a usual 2D display due to the ability of input and output device. The usual X-ray detector as an input device can get only the intensity information of X-ray penetrated targets and the usual display as an output device can display only 2D images. These devices have not enough ability for supplying more novel information. In our laboratory, we have developed the special X-ray detector which can detect the intensity and the energy information of X-ray photon by detecting photon energy individually; it is called The photon counting type X-ray detector. we reported in 1,2,3,4. On the other hand, we have developed the mono-color holographic image reconstruction system for a 3D display. Therefore, we tried to build the complete 3D input/output (I/O) CT system by use these technologies and compose the full-color holographic image reconstruction system for representing the energy information from X-ray detector. The full-color holographic image reconstruction system is already reported by Ito group 5,6, and Sato group 9. These techniques make possible to obtain 3D image easily by simple system, and get the full-color 3D image by synthesizing the three primary colors. 2. PURPOSE In this paper, we aimed to build the multi-color holographic image reconstruction system with the simple optical setup and the simple calculation method. In order to treat the X-ray CT data from the measuring system as an input data, the electro-holography with the computer generated holography was employed. The various calculation methods of the CGH are reported 7,8,10. The liquid crystal display (LCD) panel was used as a spatial light modulator (SLM) instead of a light sensitive film, this method reported in 5,11. Moreover, in order to reconstruct the multi-color image, the home projector was fixed as reconstruction system which has three LCDs Further author information: (Send correspondence to Akifumi Koike) koike@nvrc.rie.shizuoka.ac.jp, Telephone: Eighth International Conference on Correlation Optics, edited by Malgorzata Kujawinska, Oleg V. Angelsky, Proc. of SPIE Vol. 7008, 70081H, (2008) X/08/$18 doi: / SPIE Digital Library -- Subscriber Archive Copy Proc. of SPIE Vol H-1

Figure 2. Measured small motor by multi-slice CT : The small motor measured 16 slice, and converted into the CT value by a normal CT method.

2 Cu Filter(O2mm) I 4OkV,6011A U CdTe detector (I 28ch) Figure 1. X-ray CT measurement system : The 128ch CdTe detector detect the intensity and energy information of photon which comes through targets on the stage, while incident the X-ray from the X-rays tube. Figure 2. Measured small motor by multi-slice CT : The small motor measured 16 slice, and converted into the CT value by a normal CT method. Those data displayed by 3D Computer Graphics with OpenGL on a normal PC. for Red and Green, Blue color respectively. In measuring a target by X-ray CT, a small motor was measured as the target object by multi-slice X-ray CT method, and only one threshold for the energy value is employed for decreasing the noise which appears in low energy. It makes possible to measure the slight different of the CT value which depends on the density and the atomic number of materials in the high SNR condition. In this paper, the CT value means the mapping of the attenuate coefficiency of X-rays that penetrated a material. In creating a hologram that is displayed to the LCD, the interference equation, which is discretized and eliminated the amplitude information, was calculated and it converts into the binary hologram for simplify of the display. 3. PHOTON ENERGY DISCRIMINATION X-RAY 3D CT The measurement system is composed with the X-rays tube and the cupper (Cu) filter and the stage, and 128ch CdTe detector as shown in Fig.1 As the X-rays tube have wide band spectrum, it can detect the difference of spectrum between before and after of the photon penetrated the small motor, which corresponding to the incident X-ray energy and the attenuate coefficient depend on the material. Moreover, the CdTe detector can detect each photon energy individually with five levels threshold, it can obtain the energy spectrum (The histogram of each photon energy), that is to say, it can discriminate the energy information. The Cu filter makes improvement of the detection characteristics. The motor was imaged by multi-sliced imaging method, and the number of slices was 16. After the measurement, the data were computed by CT software with some data processing, then, the 3D CT data have boxels. The small motor measured and processed some process, and display by the computer graphics image rendered by opengl with Java3D, which it is composed by gathering of the small spheres. display by 3D CG with a computer is shown in Fig.2. In render processing, the small value of the CT data were eliminated by the threshold value of photon energy to get a clear image. Finally, the total points of this CT data were 86,216 points. Proc. of SPIE Vol H-2

$Holographic phenomenon : The incident light wave is diffracted by an object, and propagate to hologram plane, finally, intereference with a reference light.$

3 Object plane Collimated Referencelight Ice Light Figure 3. Holographic phenomenon : The incident light wave is diffracted by an object, and propagate to hologram plane, finally, intereference with a reference light. These phenomena creates a intereference fringe (a hologram). 4. HOLOGRAPHY 4.1 The Electro-holography The electro-holography is one of the methods to obtain holographic reconstruction images. This method uses an electric device as a spatial light modulator for displaying the hologram instead of a light sensitive film. In this examination, a liquid crystal display (LCD) panel is used as it, because of the simplification to drive 2D pixel structure, and it can get easily for commercial. Moreover, in this examination, the hologram data for displaying onto a LCD are created by the computer generated holography. It can input digital data easily due to use the computer. Therefore, it is suitable for the CT data. 4.2 The Computer Generated Holography The computer generated holography (CGH) is the technique of simulation of the light propagation and diffraction, and interference by a computer. There are some method for an object representation model, point oriented model and surface model and etc. In our simulator use point oriented model, because the CT data have boxel model. It assumes that an object is composed with gathering many points same as CT data. In electro-holography, a hologram plane is also composed with gathering many points, these are composed with pixel structure, because it is corresponded to a LCD. Therefore, the simulator calculates the light wave theorem between an object point and a hologram plane point respectively. The light wave is expressed with follow equation: ψ(r) = A exp(ikr φ) (1) r = (x ξ) 2 +(y η) 2 + z0 2 (2) Then, A is constant and k isthewavenumberandφ is the initial phase, and r means the distance between object and hologram plane. In Eq.(2), x, y is a coordinate on an object, and ξ,η,z 0 is a coordinate on a hologram plane. The holographic phenomenon contains three physical phenomena of light waves as shown in Fig.3. One is the diffraction due to through an object which is assuming that the gathering of apertures; the diffraction angle depends on the size of aperture. after that, this diffracted light wave propagate to a hologram plane from an object (It is called an object light wave). At this time, a reference light wave which can interference with the object light wave incident into a hologram plane, the interference appear on a hologram plane. Then, an interference fringe pattern is created at a hologram plane; it is called hologram, and it includes the phase and the intensity information between these light waves. The diffraction phenomenon express with follow equation: ψ dif (ξ,η) = A exp(ikr) ds(x, y) (3) iλ r S Proc. of SPIE Vol H-3

4 LCD Beam Splitter 4 N LLJ SOOmmI Controller / Field Lens 4 (1300mm) Collimator Lens (f300mm) Pinhole Filter LEL? View Point Figure 4. Mono-color reconstruciton optical setup : The light from LED light source is filtered by the pinhole filter and it is assumed as the point light source. This light collimated to parallel light by the collimater lens, and incident into the LCD which is displayed a computed hologram. It is diffracted and refrected by hologram on the LCD, and propagate to the field lends. Finally the 3D object imaged on the field lends. Then, λ is wave length and S is the area of aperture, and ds is the minute parts of area on an aperture. The interference phenomenon express with follow equation: I(ξ,η) = ψ dif + ψ ref 2 (4) I (ξ,η) = AB exp(ik(r r )) ds(x, y) (5) iλ S r Then, the ψ ref means the reference light wave, and r is distance from the original point on hologram plane. this reference light wave is expressed same fomula as Eq.(1). Four term contains in I(ξ,η), I is one of a interference term which corresponding to the real image. It can get the hologram to calculate this equation. However, it cannot be calculated by a computer due to it is concrete equation. Therefore, it has to be discretized as follow equation: I n = AB iλ M exp ( ik(r r ) ) m In this equation, m meansapointonanobject,andm is its total of points, and n means a point on a hologram plane. Therefore I n means the intensity of a point n on hologram plane. 4.3 Reconstruction System The mono-color holographic image reconstruction optical setup is very simple as shown in Fig.4. In this setup, the light source is a LED for direct obtaining with eyes. The LCD is DILA-SX070 made by JVC, which LCD is reflective type LCD fabricated by LCOS method. The resolution is pixels and its pixel pitch is 10.4(H)µm 10.4(V) µm, and the effective size of the display is 14.6mm(H) 10.9mm(V), the ratio of aperture of each pixel is 93%. The mono-color holographic image reconstructed by the above setup is shown in Fig.5. This reconstruction image is the small motor reconstructed with the green LED. The data of the small motor are imaged by X-ray 3D CT, and it was processed the edge extraction by a software method. Then, the surface data and a part of internal data were extracted from the original data. 5. EXAMINATION AND RESULT In order to achieve the multi-color holographic reconstruction, the reconstruction optical setup with the home projector (Canon: SX50) which has three LCDs for Red and Green, and Blue was composed, and it is shown in Fig.6. These LCDs are same as the LCD of the mono-color reconstruction optical setup (Fig.4), and optical elements which need not this examination were removed. r (6) Proc. of SPIE Vol H-4

Y I x a) The mono-color reconstruction b) The axis of c) The input image image of small motor imaged the reconstruction image. that is reduced the by multi slice X-ray CT. points by sampling.

Di LCD_G chroic Mirror Mirror N BS: Beam Splitter WP: Wavelength Selective Phase Plate LED Field Lens Figure 6.

5 Y I x a) The mono-color reconstruction b) The axis of c) The input image image of small motor imaged the reconstruction image. that is reduced the by multi slice X-ray CT. points by sampling. Figure 5. Mono-color motor reconstruction image : This is the image of small motor tilted 9 degree from the vertical standing state by the X axis shown in Fig.5b. The input data are shown in Fig.5c. Di LCD_G chroic Mirror Mirror N BS: Beam Splitter WP: Wavelength Selective Phase Plate LED Field Lens Figure 6. Multi-color reconstruction optical setup : The light from LED is filted and collimated to parallel light, and arranged the polarizing direction by the polarizing film. This light split into three lights by the dichroic mirror and the beam splitter, and the wavelength sensitive phase plate. Finally, each of light incident into the LCDs for red, green, blue respectively, and these are outputed to the field lens simultaneously, and piled up. Proc. of SPIE Vol H-5

a) High CT value parts with red b) Middle CT value parts with green c) Low CT value patrs with blue d) High, Middle, Low CT value parts with red, gree, blue Figure 7.

7a),b),c) is each of part reconstruction image, and d) is all parts reconstruction image The small motor measured by multi-slice X-ray CT was used as input data (Fig.

6 a) High CT value parts with red b) Middle CT value parts with green c) Low CT value patrs with blue d) High, Middle, Low CT value parts with red, gree, blue Figure 7. Multi-color reconstruction images: The small motor was reconstructed with three colors corresponding to the enegry level. High energy level is red, Middle is green, low is blue respectively. Fig.7a),b),c) is each of part reconstruction image, and d) is all parts reconstruction image The small motor measured by multi-slice X-ray CT was used as input data (Fig.2), and it was split into three parts by intensity of its CT value; high, middle, low. These data had about 40,000, 7500, 1000 points respectively, then it was reduced its points by a sampling method, because it was too huge number of points to finish the CGH calculation in an effective time. The calculation equation in the CGH is as follow: I n = 1 λζ n M m ( exp k ) (x m ξ n ) 2 +(y m η n ) 2 +(z m ζ n ) 2 ) This equation is almost same as Eq.(6), the difference is it expresses the object as 3D object with the coordinate ζ. This equation has no amplitude information of light waves, however, the shape information depends on phase information dominantly in image reconstructions, the result is reported in. 12 Therefore, it can obtain enough quality images calculated with above equation to recognize its shape. Moreover, the fact that the binary hologram which has only two values, white and black, can reconstruct enough quality is known. And it makes easy to display a hologram on the LCD by without being necessary to consider the detail of LCD specific color characteristics. However these methods make impossible to reconstruct full-color images by piling up primary colors of light waves, because it cannot calibrate the intensity of each of the light wave. But, in this examination, it was employed these method because we aim to reconstruct X-ray 3D CT holographic images by multi-color hologram for confirming basics of our system. There is one more problem for multi-color reconstruction; it is gap of reconstruction position of each color image. In order to resolve it, the calibration method by selecting region from a large size hologram 9 was employed. The reconstructed X-ray 3D CT image of the small motor by these processes could obtain and it is shown in Fig.7. The high, middle, low CT value reconstructed with red, gree, blue color respectively, and the multi-color image reconstructed these parts simltaneously is shown in this figure. The high CT value parts (Fig.7a) is the highest density in the small motor, because it need high energy of photon to penetrate a high density parts and a deep position parts. In middle and low CT value, it can explain (7) Proc. of SPIE Vol H-6

7 the same theory. 6. DISCUSSION The multi-color reconstruction image (Fig.7d) could recognize the internal structure of the small motor easier than the mono-color reconstruction (Fig.5), because the difference of color between three parts. Moreover, this method can display any range of the CT values individualy with several colors, and the CT value depends on the density of the part of objects. Therefore, it can separate a object into some parts of the density layer in a general case. In this examination, it was used only two energy band of fifth, and the lower band was dropped for reducing noizes which appear at low energy bands. Therefore, it will be able to display the true phisycal phenomenon in the X-ray detection, and represent more effective 3D information, if these energy bands was used fully, because the input data become direct information of the photon energy. Moreover, it was used only three primary colors, but this reconstruction system has ability to reconstruct full-color images by piling up three primary colors, if the non-approximation method was employed for calculating holograms. However, the LCD panel has not enouch ability to achieve these things, in the current reconstruction system. At first, the pixel-pitch of the LCD is too big to display high quality multi-color 3D images, because the diffraction angle depends on the pixel-pitch which is assumed that the aperture. The equation of this is as follow: 2d sin θ = nλ (8) ( ) nλ θ = arcsin (9) 2d Eq.(8) is Bragg equation. Then, d is the pixel-pitch and theta is diffraction angle, and n is index of diffraction rank, and λ is wavelength. Moreover, the display size is too small for a practical size images reconstruction. In the current system, the field lens expand the image size, but it reduce the viewing angle. To resolve these problem, it must be developed a more novel SLM device which is small pixel-pitch and large size. 7. CONCLUTION The multi-color holographic reconstruction image of X-ray 3D CT was obtained by the simple optical setup that we developed. The input data of X-ray 3D CT was measured by the X-ray CT measurement system. In this examination, the target object was the small motor, and imaged 16 slices by multi-slice imaging method. This data were separated into three parts by the CT value; High, Middle, Low, and processed point reduction by sampling method for effective calculation times. The simple multi-color reconstruction optical setup was composed with home projector, and the reconstruction image was obtaind. It was shown that the multi-color holographic images reconstrution is effective for X-ray 3D CT data, to represent internal structures and depth information. REFERENCES 1. T. Aoki, Y. Ishida, H. Morii, Y. Tomita, G. Ohashi, J. Temmyo, Y. Hatanaka, Super-resolution X-ray imaging by CdTe discrete detector arrays, Proc. SPIE, 5922, pp T, T. Aoki, Y. Ishida, Y. Makino, G. Ohashi, Y. Tomita, H. Morii, J. Temmyo, Y. Hatanaka, Photon Counting Type X-ray Imager with Energy Distinction, Proceedings of The 12th International Display Workshop in conjunction with Asia Display 2005, pp , T. Aoki, V. A. Gnatyuk, A. Nakamura, Y. Tomita, Y. Hatanaka, J. Temmyo, Study of a CdTe high-energy radiation imaging device fabrication by excimer laser processing, Phys. Stat. Sol. C, 1, pp , M. Niraula, A. Nakamura, T. Aoki, Y. Tomita, Y. Hatanaka, Diode-Type CdTe Strip and Linear Array Detectors for Gamma-Ray Detection and Imaging, IEEE Trans. on Nulcear Sci., 49, pp , 2002 Proc. of SPIE Vol H-7

8 5. T.Ito, T.Shimobaba, H.Godo, M.Horiuchi, Holographic reconstruction with a 10-µm pixel-pitch reflective liquid-crystal display by use of a light-emitting diode reference light, Opt.Letters, 27, 16, pp , A.Shiraki, Y.Abe, T.Tanaka, A.Neo, N.Masuda and T.Ito, Simplified Holographic Reconstruction System Using Graphics Prosessing Unit and Projector, The Journal of The Institute of Image Information and Television Engineers, 61, 4, pp , T.Shimobaba, A.Shiraki, N.Masuda, and T.Ito, Electroholographic display unit for three-dimensional display by use of special-purpose computational chip for holography and reflective LCD panel, OPTICS EXPRESS, 13, 11, pp , N.Masuda, K.Yoshimura, A.Shiraki, and T.Ito, Special-purpose computer HORN-5 for a real time electroholography, OPTICS EXPRESS, 13, 6, pp , K.Takano, K.Obana, K.Wada, T.Tanaka, and K.Sato, Development of a Full-Color Electro-holographic Display Using LEDS, The Journal of The Institute of Image Information and Television Engineers, 58, 3, pp , H.Yoshikawa, S.Iwase, and T.Oneda, Fast Computation of Fresnel Holograms employing Difference, Proc.SPIE, 3956, pp , R.Tudela, I.Labastida, E.Martin-Badosa, S.Vallmitjana, I.Juvells, A.Carnicer, A simple method for displaying Fresnel holograms on liquid crystal panels, Optics Communication, 214, pp , A.V.Oppenheim, J.S.Lim, The Importance of phase in signals, Proc.IEEE, 69, 5, pp. 529, 1981 Proc. of SPIE Vol H-8

Invited Paper. Nukui-Kitamachi, Koganei, Tokyo, , Japan ABSTRACT 1. INTRODUCTION

Invited Paper. Nukui-Kitamachi, Koganei, Tokyo, , Japan ABSTRACT 1. INTRODUCTION Invited Paper Wavefront printing technique with overlapping approach toward high definition holographic image reconstruction K. Wakunami* a, R. Oi a, T. Senoh a, H. Sasaki a, Y. Ichihashi a, K. Yamamoto