X CT JASRI / SPring /7/4 1

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X CT JASRI / SPring-8 2004/7/4 1

( )...3...3 ( )...4...15...30 2

( ) CT q001.img q002.img, d01.img d02.img, output.log q???.img output.log ( ) ImagePro HiPic tiff q001.tif q002.tif, d01.tif d02.tif, output.log ct_cbp.exe ct_sino.exe ct_sino_tif.exe rec2tif.exe sino2tif.exe img_ave.exe img2tif.exe sfa.exe srec.exe tif_h2o.exe tif2hst.exe (exe ) mkdark.bat reconst.bat sinogram.bat ( ) ( ) filtered back projection method ct_fbp.exe (2004.2.4) ( ) DOS 3

( ) ct_test.lzh windows (ct_manual.lzh) ct_test.txt a. c: ct d: ct_data dummy (path) path 4

b. d01.img d02.img q001.img q201.img output.log ( ) lzh mkdark.bat dark.img OK 5

c. 300(W) 100(H) 0 99 (50 layer) sinogram.bat sino0050.tif IrfanView 1 180 0.24 750 750pixel 6

d. (50 layer) rec0050.tif IrfanView 7

( 0 ) X ( ) ( ) X (Linear Absorption Coefficient, LAC) LAC = 8647.235857 ( 0.839662) 8647.235857-0.839662 conversion constants TIFF CT 16bit ring artifact 8

501.5 510.0 DOS LAC 9

e. D: ct_data dummy>img_ave d01.img d02.img dark.img read d01.img d01.img read d02.img d02.img output dark.img dark.img D: ct_data dummy>ct_sino 50 q dark.img nshot = 180, NI0 = 19, total = 201 store sinogram 0.953000 / sec 180 I 0 19 201 D: ct_data dummy>sino2tif 8 Image size: 300 x 180 300(W) 180(H) MAX and min: 0.580355 to 0.000000 CT image to: 8 bits TIFF. TIFF bit Stored to: sino0050.tif Rotation axis: 501.455054 D: ct_data dummy>sino_conv 510. 510. D: ct_data dummy>ct_cbp Width of image : 300 Number of Projection : 180 Rotation center : 151.0000000 reconstruction : 4 / sec D: ct_data dummy>rec2tif Image size: 300 x 300 MAX and min: 10.113399 and -3.240130 LAC CT image to: 16 bits TIFF. TIFF bit Conv. const.: 10 0.000000 LAC Pixel size: 5.830000 5.83µm Stored to: rec0050.tif f. D: ct_data dummy>sfa.exe 50 499. 503. 1.0 5.83 > 50.bat 10

50.bat 50 499 503 1.0pixel 50.bat 1pixel 5.83µm *** ct_sino 50 q dark.img copy s0050.sin tmp.sin sino_conv 499.000000 ct_cbp rec2tif 16 5.830000 ren rec0050.tif 0050_04990.tif copy tmp.sin s0050.sin sino_conv 500.000000 ct_cbp rec2tif 16 5.830000 ren rec0050.tif 0050_05000.tif copy tmp.sin s0050.sin sino_conv 501.000000 ct_cbp rec2tif 16 5.830000 ren rec0050.tif 0050_05010.tif copy tmp.sin s0050.sin sino_conv 502.000000 ct_cbp rec2tif 16 5.830000 ren rec0050.tif 0050_05020.tif copy tmp.sin s0050.sin sino_conv 503.000000 ct_cbp rec2tif 16 5.830000 ren rec0050.tif 0050_05030.tif del tmp.sin *** 50 s0050.sin tmp.sin 499.0 CBP TIFF rec0050.tif 0050_04950.tif tmp.sin s0050.sin 500.0 ( ) tmp.sin ( ) D: ct_data dummy>50.bat 0050_04990.tif 0050_05030.tif TIFF 11

0050_05010.tif ( ) 0050_04990.tif 0050_05030.tif 0050_05010.tif 50 501.0 0.5pixel g. ct_sino.exe sino_conv.exe ct_cbp.exe rec2tif.exe D: ct_data dummy>srec 5 501. 10 502. 5.83 > 5-10.bat 5-10.bat 5 501 10 502 (sfa.exe ) 5.83µm D: ct_data dummy> 5-10.bat rec0005.tif rec0010.tif 16bit tiff h. 8bit 16bit tiff 8bit rec2tif 16bit (rec????.tif) 8bit tiff (ro????.tif) D: ct_data dummy>tif_h2o 100 200 0.0 2.0 rec0100.tif rec0200.tif ro0001.tif ro0101.tif ( ) rec0100.tif ro0001.tif 8bit ro????.tif 0 0.0cm -1 255 12

2.0cm -1 D: ct_data dummy>tif_h2o 100 200 0.0 2.0 100 150 250 350 rec0100.tif rec0200.tif (100,150)-(250,350) ro0001.tif ro0101.tif 0.0-2.0cm-1 8bit i. 8bit 8bit ( ) 16bit tiff rec0050.tif 16bit (7 ) D: ct_data dummy>tif2hst rec0050.tif rec0050.hst rec0050.hst rec0050.hst rec0050.hst 0.010000 15510 14990 0.020000 15468 14883 15000 0.030000 15482 14551 0.040000 15428 14240 10000 0.050000 15310 13806 0.060000 14795 13163 0.070000 14769 12964 5000 0.080000 14240 12121 0.090000 14180 11780 0-5 0 5 0.100000 13419 10971 Linear absorption coefficient (cm -1 ) ( ) Number of pixel rec0050.hst (cm -1 ) 13

0cm -1 5cm -1 X j. TIFF TIFF IrfanView CT http://www.irfanview.com/ 16bit tiff Image Tool http://ddsdx.uthscsa.edu/dig/itdesc.html k. II ueken@spring8.or.jp 14

Windows (exe ) X (CT ) a) img_ave.exe img (HiPic ) %img_ave dark1 dark2 dark dark1 : ( ) dark2 : ( ) dark : ( ) 1. d: data 010226e> img_ave d01.img d02.img dark.img 2. d: data 010226e> img_ave d01.img d02.img d03.img dark.img 1. d01.img d02.img dark.img 2. d01.img d02.img d03.img dark.img 15

b) ct_sino.exe and ct_sino_tif.exe CT ( ) ct_sino.exe.img ct_sino_tif.exe TIFF %ct_sino layer (head) (dark) layer head dark : (layer) : ( q ) : ( dark.img ) 1. d: data 010226e> ct_sino 100 2. d: data 010226e> ct_sino 100 q d01.img 3. d: data 010226e> ct_sino 100 r d00.img 1. 100 q001.img q002.img dark.img 2. 1. 100 1 d01.img 3. d00.img r001.img r002.img. ct_sino.exe (s????.sin layer ) sino.tmp sino.tmp layer (pixel ) TIFF (sinogram) sino.tmp 1000 720 0100 layer 461.076695 16

c) ct_cbp.exe or ct_fbp.exe ct_sino.exe layer %ct_cbp 1. d: data 010226e> ct_cbp 1. ct_sino.exe ct_fbp.exe (double ) (r????.rec layer ) rec.tmp RECLBL (http://cfi.lbl.gov/) rec.tmp 0100 layer 1000 720 900 461.0000 2 filter filter 1. HAN 2. HAM 3. RAMP 4. PARZN 5. BUTER ct_cbp.exe HAN 17

d) rec2tif.exe ct_cbp.exe double 8bit or 16bit TIFF ct_cbp.exe (NDIMU NDIMU) %rec2tif (bit) (delta) (div) (base) bit delta div base : 8 or 16 bit ( 16bit) : pixel ( 5.83µm) : LAC ( )(bit LAC ) : LAC ( CT ) 1. d: data 010226e> rec2tif 2. d: data 010226e> rec2tif 8 12. 3. d: data 010226e> rec2tif 16 5.8 100 10. 1. rec.tmp double TIFF 16bit 2. TIFF 8bit 1pixel 12µm 3. TIFF 16bit ct_cbp.exe rec.tmp TIFF tif_inf.exe bit 1 pixel (div) (base) (1-5) LAC(Linear Absorption Coefficient ) LAC = div + base 18

e) sino2tif.exe ct_sino.exe double 8bit or 16bit TIFF %sino2tif (bit) bit : 8 or 16 bit ( 16bit) d: data 010226e> sino2tif double 16bit TIFF ct_sino.exe sino.tmp TIFF PhotoShop WZ Editor bit (div) (base) sinogram(p=ln(i0 / I)) = div + base 19

f) img2tif.exe HiPic 8bit or 16bit TIFF %img2tif input.img output.tif from to bit input.img output.tif from to bit : (???.img) : : 8bit : 8bit : 8 or 16 bit 1. d: data 010226e> img2tif q001.img q001.tif 0 12000 8 2. d: data 010226e> img2tif q001.img q001.tif 0 0 16 1. q001.img 8bit TIFF TIFF 255 img 12000 2. img 16bit TIFF img 14bit 8bit from to 0 0 img from to 20

g) sino_conv.exe ct_sino sino.tmp %sino_conv AXIS AXIS : d: data 010226e> sino_conv 501.2 sino.tmp 501.2 (ct_sino.exe) (ct_cbp.exe) 21

h) sfa.exe or sfa_tif.exe %sfa layer from to step (delta) > output layer : from : ( ) to : ( ) step : ( ) delta : ( ) output : ( ) d: data 010226e> sfa 10 148 152 1.0 5.83 > 20.bat 10 148 152 1.0pixel 20.bat 1pixel 5.83µm 22

i) srec.exe or srec_tif.exe %srec from axis1 to axis2 (delta) > output from : axis1 : ( ) to : axis2 : ( ) delta : ( ) output : ( ) d: data 010226e> srec 5 149 10 151 5.83 > 5-10.bat 5 10 5 149 10 151 5-10.bat 1pixel 5.83µm sfa.exe 23

j) tif_h2o.exe (tiff 16bit) tiff 8bit %tif_h2o sta_ly dst_ly LACmin LACmax (x1 y1 x2 y2) sta_ly : dst_ly : LACmin : 8 bit 0 (cm -1 ) LACmax : 8 bit 255 (cm -1 ) x1 : y1 : x2 : y2 : 1. d: data 010226e> tif_h2o 100 200 0.0 2.0 2. d: data 010226e> tif_h2o 100 200 0.0 2.0 100 150 200 350 1. 100(rec0100.tif) 200(rec0200.tif) 8 bit tiff ro0001.tif ro0101.tif ro????.tif 0 0.0cm -1 255 2.0cm -1 2. 1 16bit (100,150)-(200,350) 101x201 rec????.tif ( ) rec2tif.exe tif_h2o.exe tiff 16bit 8bit tif_conv.exe 24

k) tif2hst.exe (tiff 16bit or 8bit) %tif2hst input.tif outputfile input.tif outputfile : : d: data 010226e> tif2hst rec0050.tif rec0050.hst rec0050.tif rec????.tif ( ) rec2tif.exe tif_h2o.exe (cm -1 ) 15000 rec0050.hst 0.010000 15510 14990 10000 0.020000 15468 14883 0.030000 15482 14551 0.040000 15428 14240 5000 ( ) 0-5 0 5 Linear absorption coefficient (cm -1 ) Number of pixel 25

l) tif_conv.exe tiff 16bit 8bit %tif_conv input.tif output.tif destbit input.tif output.tif destbit : : : bit (8 or 16) 1. d: data 010226e> tif_conv test12.tif test16.tif 16 2. d: data 010226e> tif_conv test12.tif test8.tif 8 3. d: data 010226e> tif_conv test16.tif test8.tif 8 1. test12.tif(12bit) test16.tif(16bit) 2. test12.tif(12bit) test8.tif(8bit) 3. test16.tif(16bit) test8.tif(8bit) 16bit 8bit 12bit 8bit 8bit 16bit 12bit 16bit 8bit 16bit 26

m) tif_inf.exe tif %tif_inf input input : d: data 010226e> tif_int rec0300.tif d: data 010226e> tif_int sino0300.tif rec0300.tif sino0300.tif (CT ) 1. 2. 3. 4. 5. 6. (div) 7. (base) 8. 9. 1. 2. 3. (= ) 4. 5. (div) 6. (base) 7. ( ) 27

Windows a). mkdark.bat mkdark.bat img_ave d01.img d02.img dark.img d01.img d02.img reconst.bat ct_sino %1 q dark.img sino_conv %2 ct_cbp rec2tif 8 (%1 ) layer (%2) rec2tif 8bit TIFF sinogram.bat ct_sino %1 q dark.img sino2tif 8 (%1) layer sino2tif 8bit TIFF 28

windows98 c: autoexec.bat **** SET PATH=C: PROGRA~1 platex bin;"%path%" **** c: ct **** SET PATH=c: ct;c: PROGRA~1 platex bin;"%path%" **** c: autoexec.bat SET PATH=c: ct;"%path%" path DOS path ( ) windows 2000 windowsxp path ;c: ct path 29

CT Filtered Back Projection projection X x p(x,θ) 1 { p ( x', θ ) = ln( I0 / I) = µ ( x, y) dy' pˆ ( ω, θ ) = p( x', θ ) exp( iωx' ) dx' pˆ ( ω, θ ) = µ ( x, y) dy' exp( iωx' ) dx' x' = xcosθ + ysinθ y' = xsinθ + y cosθ pˆ ( ω, θ ) = µ ( x, y) exp( iωx cosθ iωy sin θ ) dx' dy' = ( x, y) exp( iωx cos θ iωy sin θ ) dxdy Jacobian, J =1 1 2 3 µ 4 y' projection y Fourier transform v x' x u object space domain Frequency domain 30

{ ω ω x y = ω cos θ = ω sin θ µ (x, y) pˆ (, θ ) ˆ( µ ω, ω ) ) p' ( x', θ 1 p '( x', θ ) = pˆ( ω, θ ) exp( iωx') g( ω) dω 2π g( ω ) = ω g(ω) ˆ( ω, ω ) = µ ( x, y) exp( iω x iω y dx dy µ 5 x y x y ) ω = x y 1 µ ( x, y) = ˆ( µ ωx, ωy) exp( iωxx + iωy y) dωx dω 2 y (2π ) 5 1 = pˆ( ω, θ) exp( iω xx + iω y y) dω x dω 2 y (2π ) 1 = p ˆ ( ω, θ ) exp( iωx' ) ω dω dθ 2 (2π ) 2π 1 = p'( x', θ ) dθ 2π 0 ω Filtered Back Projection pˆ ( ω, θ ) = p( x', θ ) exp( iωx' ) dx' p '( x', θ ) = pˆ( ω, θ ) exp( iωx') g( ω) dω π µ ( x, y) = p' ( x cos θ + y sin θ, θ ) dθ 0 31

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