Abstract

The camera lens diaphragm is an important component in a noncontact optical imaging system and has a crucial influence on the images registered on the CCD camera. However, this influence has not been taken into account in the existing free-space photon transport models. To model the photon transport process more accurately, a generalized free-space photon transport model is proposed. It combines Lambertian source theory with analysis of the influence of the camera lens diaphragm to simulate photon transport process in free space. In addition, the radiance theorem is also adopted to establish the energy relationship between the virtual detector and the CCD camera. The accuracy and feasibility of the proposed model is validated with a Monte-Carlo-based free-space photon transport model and physical phantom experiment. A comparison study with our previous hybrid radiosity-radiance theorem based model demonstrates the improvement performance and potential of the proposed model for simulating photon transport process in free space.

© 2010 Optical Society of America

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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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2010 (1)

2009 (3)

H. K. Kim and A. H. Hielscher, “A PDE-constrained SQP algorithm for optical tomography based on the frequency-domain equation of radiative transfer,” Inverse Probl. 25, 015010(2009).
[CrossRef]

S. R. Arridge and J. C. Schotland, “Optical tomography: Forward and inverse problems,” Inverse Probl. 25, 123010 (2009).
[CrossRef]

X. Chen, X. Gao, X. Qu, J. Liang, L. Wang, D. Yang, A. Garofalakis, J. Ripoll, and J. Tian, “A study of photon propagation in free-space based on hybrid radiosity-radiance theorem,” Opt. Express 17, 16266–16280 (2009).
[CrossRef] [PubMed]

2008 (2)

D. G. Fischer, S. A. Prahl, and D. D. Duncan, “Monte Carlo modeling of spatial coherence: free space diffraction,” J. Opt. Soc. Am. A 25, 2571–2581 (2008).
[CrossRef]

J. Tian, J. Bai, X. Yan, S. Bao, Y. Li, W. Liang, and X. Yang, “Multimodality molecular imaging,” IEEE Eng. Med. Biol. Mag. 27, 48–57 (2008).
[CrossRef] [PubMed]

2007 (4)

2006 (1)

2005 (2)

V. Ntziachristos, J. Ripoll, L. V. Wang, and R. Weissleder, “Looking and listening to light: the evolution of whole-body photonic imaging,” Nat. Biotechnol. 23, 313–320 (2005).
[CrossRef] [PubMed]

R. B. Schulz, J. Peter, W. Semmler, C. D’ Andrea, G. Valentini, and R. Cubeddu, “Quantifiability and image quality in non-contact fluorescence tomography,” Proc. SPIE 5859, 58590Z (2005).
[CrossRef]

2004 (2)

J. Ripoll and V. Ntziachristos, “Imaging scattering media from a distance: theory and applications of non-contact optical tomography,” Mod. Phys. Lett. B 18, 1403–1431 (2004).
[CrossRef]

H. Li, J. Tian, F. Zhu, W. X. Cong, L. V. Wang, and G. Wang, “A Mouse Optical Simulation Environment (MOSE) to investigate bioluminescent phenomena in the living mouse with the Monte Carlo method,” Acad. Radiol. 11, 1029–1038(2004).
[CrossRef] [PubMed]

2003 (3)

J. Ripoll, R. B. Schulz, and V. Ntziachristos, “Free-space propagation of diffuse light: theory and experiment,” Phys. Rev. Lett. 91, 103901 (2003).
[CrossRef] [PubMed]

R. B. Schulz, J. Ripoll, and V. Ntziachristos, “Non-contact optical tomography of turbid media,” Opt. Lett. 28, 1701–1703(2003).
[CrossRef] [PubMed]

R. Weissleder and V. Ntziachristos, “Shedding light onto live molecular targets,” Nat. Med. 9, 123–128 (2003).
[CrossRef] [PubMed]

2002 (1)

M. Aggarwal and N. Ahuja, “A pupil-centric model of image formation,” Int. J. Comput. Vision 48, 195–214 (2002).
[CrossRef]

2001 (1)

B. W. Rice, M. D. Cable, and M. B. Nelson, “In vivo imaging of light-emitting probes,” J. Biomed. Opt. 6, 432–440 (2001).
[CrossRef] [PubMed]

1999 (1)

S. R. Arridge, “Optical tomography in medical imaging,” Inverse Probl. 15, R41–R93 (1999).
[CrossRef]

1995 (1)

L. V. Wang, S. L. Jacques, and L. Q. Zheng, “MCML-Monte Carlo modeling of photon transport in multi-layered tissues,” Comput. Methods Programs Biomed. 47, 131–146 (1995).
[CrossRef] [PubMed]

Aggarwal, M.

M. Aggarwal and N. Ahuja, “A pupil-centric model of image formation,” Int. J. Comput. Vision 48, 195–214 (2002).
[CrossRef]

M. Aggarwal and N. Ahuja, “A new imaging model,” in Proceedings of the International Conference on Computer Vision (IEEE, 2001), pp. 82–89.

Ahuja, N.

M. Aggarwal and N. Ahuja, “A pupil-centric model of image formation,” Int. J. Comput. Vision 48, 195–214 (2002).
[CrossRef]

M. Aggarwal and N. Ahuja, “A new imaging model,” in Proceedings of the International Conference on Computer Vision (IEEE, 2001), pp. 82–89.

Arridge, S. R.

S. R. Arridge and J. C. Schotland, “Optical tomography: Forward and inverse problems,” Inverse Probl. 25, 123010 (2009).
[CrossRef]

R. Elaloufi, S. R. Arridge, R. Pierrat, and R. Carminati, “Light propagation in multilayered scattering media beyond the diffusive regime,” Appl. Opt. 46, 2528–2539 (2007).
[CrossRef] [PubMed]

S. R. Arridge, “Optical tomography in medical imaging,” Inverse Probl. 15, R41–R93 (1999).
[CrossRef]

Bai, J.

J. Tian, J. Bai, X. Yan, S. Bao, Y. Li, W. Liang, and X. Yang, “Multimodality molecular imaging,” IEEE Eng. Med. Biol. Mag. 27, 48–57 (2008).
[CrossRef] [PubMed]

Bao, S.

J. Tian, J. Bai, X. Yan, S. Bao, Y. Li, W. Liang, and X. Yang, “Multimodality molecular imaging,” IEEE Eng. Med. Biol. Mag. 27, 48–57 (2008).
[CrossRef] [PubMed]

Cable, M. D.

B. W. Rice, M. D. Cable, and M. B. Nelson, “In vivo imaging of light-emitting probes,” J. Biomed. Opt. 6, 432–440 (2001).
[CrossRef] [PubMed]

Carminati, R.

Chen, X.

Cong, W. X.

H. Li, J. Tian, F. Zhu, W. X. Cong, L. V. Wang, and G. Wang, “A Mouse Optical Simulation Environment (MOSE) to investigate bioluminescent phenomena in the living mouse with the Monte Carlo method,” Acad. Radiol. 11, 1029–1038(2004).
[CrossRef] [PubMed]

Cubeddu, R.

R. B. Schulz, J. Peter, W. Semmler, C. D’ Andrea, G. Valentini, and R. Cubeddu, “Quantifiability and image quality in non-contact fluorescence tomography,” Proc. SPIE 5859, 58590Z (2005).
[CrossRef]

D’ Andrea, C.

R. B. Schulz, J. Peter, W. Semmler, C. D’ Andrea, G. Valentini, and R. Cubeddu, “Quantifiability and image quality in non-contact fluorescence tomography,” Proc. SPIE 5859, 58590Z (2005).
[CrossRef]

Deliolanis, N.

Du, B.

B. Du and J. Wang, Electron Optics (Tsinghua University, 2002).

Duncan, D. D.

Economou, E. N.

Elaloufi, R.

Fischer, D. G.

Gao, F.

D. Qin, H. Zhao, Y. Tanikawa, and F. Gao, “Experimental determination of optical properties in turbid medium by TCSPC technique,” Proc. SPIE 6434, 64342E (2007).
[CrossRef]

Gao, X.

Garofalakis, A.

Hanrahan, P.

C. Kolb, D. Mitchell, and P. Hanrahan, “A realistic camera model for computer graphics,” in Proceedings of the 22nd Annual Conference on Computer Graphics and Interactive Techniques (ACM, 1995), pp. 317–324.

Hielscher, A. H.

H. K. Kim and A. H. Hielscher, “A PDE-constrained SQP algorithm for optical tomography based on the frequency-domain equation of radiative transfer,” Inverse Probl. 25, 015010(2009).
[CrossRef]

Hyde, D.

Jacques, S. L.

L. V. Wang, S. L. Jacques, and L. Q. Zheng, “MCML-Monte Carlo modeling of photon transport in multi-layered tissues,” Comput. Methods Programs Biomed. 47, 131–146 (1995).
[CrossRef] [PubMed]

Kim, H. K.

H. K. Kim and A. H. Hielscher, “A PDE-constrained SQP algorithm for optical tomography based on the frequency-domain equation of radiative transfer,” Inverse Probl. 25, 015010(2009).
[CrossRef]

Kioussis, D.

Kolb, C.

C. Kolb, D. Mitchell, and P. Hanrahan, “A realistic camera model for computer graphics,” in Proceedings of the 22nd Annual Conference on Computer Graphics and Interactive Techniques (ACM, 1995), pp. 317–324.

Lasser, T.

Li, H.

H. Li, J. Tian, F. Zhu, W. X. Cong, L. V. Wang, and G. Wang, “A Mouse Optical Simulation Environment (MOSE) to investigate bioluminescent phenomena in the living mouse with the Monte Carlo method,” Acad. Radiol. 11, 1029–1038(2004).
[CrossRef] [PubMed]

Li, J.

Li, Y.

J. Tian, J. Bai, X. Yan, S. Bao, Y. Li, W. Liang, and X. Yang, “Multimodality molecular imaging,” IEEE Eng. Med. Biol. Mag. 27, 48–57 (2008).
[CrossRef] [PubMed]

Liang, J.

Liang, W.

J. Tian, J. Bai, X. Yan, S. Bao, Y. Li, W. Liang, and X. Yang, “Multimodality molecular imaging,” IEEE Eng. Med. Biol. Mag. 27, 48–57 (2008).
[CrossRef] [PubMed]

Liao, Y.

Q. Tian, Y. Liao, and L. Sun, Engineering Optics (Tsinghua University, 2004).

Lu, B.

Mamalaki, C.

Meyer, H.

Mitchell, D.

C. Kolb, D. Mitchell, and P. Hanrahan, “A realistic camera model for computer graphics,” in Proceedings of the 22nd Annual Conference on Computer Graphics and Interactive Techniques (ACM, 1995), pp. 317–324.

Nelson, M. B.

B. W. Rice, M. D. Cable, and M. B. Nelson, “In vivo imaging of light-emitting probes,” J. Biomed. Opt. 6, 432–440 (2001).
[CrossRef] [PubMed]

Ntziachristos, V.

N. Deliolanis, T. Lasser, D. Hyde, A. Soubert, J. Ripoll, and V. Ntziachristos, “Free-space fluorescence molecular tomography utilizing 360° geometry projections,” Opt. Lett. 32, 382–384 (2007).
[CrossRef] [PubMed]

H. Meyer, A. Garofalakis, G. Zacharakis, S. Psycharakis, C. Mamalaki, D. Kioussis, E. N. Economou, V. Ntziachristos, and J. Ripoll, “Noncontact optical imaging in mice with full angular coverage and automatic surface extraction,” Appl. Opt. 46, 3617–3627 (2007).
[CrossRef] [PubMed]

V. Ntziachristos, J. Ripoll, L. V. Wang, and R. Weissleder, “Looking and listening to light: the evolution of whole-body photonic imaging,” Nat. Biotechnol. 23, 313–320 (2005).
[CrossRef] [PubMed]

J. Ripoll and V. Ntziachristos, “Imaging scattering media from a distance: theory and applications of non-contact optical tomography,” Mod. Phys. Lett. B 18, 1403–1431 (2004).
[CrossRef]

J. Ripoll, R. B. Schulz, and V. Ntziachristos, “Free-space propagation of diffuse light: theory and experiment,” Phys. Rev. Lett. 91, 103901 (2003).
[CrossRef] [PubMed]

R. Weissleder and V. Ntziachristos, “Shedding light onto live molecular targets,” Nat. Med. 9, 123–128 (2003).
[CrossRef] [PubMed]

R. B. Schulz, J. Ripoll, and V. Ntziachristos, “Non-contact optical tomography of turbid media,” Opt. Lett. 28, 1701–1703(2003).
[CrossRef] [PubMed]

Peter, J.

R. B. Schultz, J. Peter, and W. Semmler, “Comparison of non-contact and fiber-based fluorescence-mediated tomography,” Opt. Lett. 31, 769–771 (2006).
[CrossRef]

R. B. Schulz, J. Peter, W. Semmler, C. D’ Andrea, G. Valentini, and R. Cubeddu, “Quantifiability and image quality in non-contact fluorescence tomography,” Proc. SPIE 5859, 58590Z (2005).
[CrossRef]

Pierrat, R.

Prahl, S. A.

Psycharakis, S.

Qin, D.

D. Qin, H. Zhao, Y. Tanikawa, and F. Gao, “Experimental determination of optical properties in turbid medium by TCSPC technique,” Proc. SPIE 6434, 64342E (2007).
[CrossRef]

Qu, X.

Ren, N.

Rice, B. W.

B. W. Rice, M. D. Cable, and M. B. Nelson, “In vivo imaging of light-emitting probes,” J. Biomed. Opt. 6, 432–440 (2001).
[CrossRef] [PubMed]

Ripoll, J.

Schotland, J. C.

S. R. Arridge and J. C. Schotland, “Optical tomography: Forward and inverse problems,” Inverse Probl. 25, 123010 (2009).
[CrossRef]

Schultz, R. B.

Schulz, R. B.

R. B. Schulz, J. Peter, W. Semmler, C. D’ Andrea, G. Valentini, and R. Cubeddu, “Quantifiability and image quality in non-contact fluorescence tomography,” Proc. SPIE 5859, 58590Z (2005).
[CrossRef]

J. Ripoll, R. B. Schulz, and V. Ntziachristos, “Free-space propagation of diffuse light: theory and experiment,” Phys. Rev. Lett. 91, 103901 (2003).
[CrossRef] [PubMed]

R. B. Schulz, J. Ripoll, and V. Ntziachristos, “Non-contact optical tomography of turbid media,” Opt. Lett. 28, 1701–1703(2003).
[CrossRef] [PubMed]

Semmler, W.

R. B. Schultz, J. Peter, and W. Semmler, “Comparison of non-contact and fiber-based fluorescence-mediated tomography,” Opt. Lett. 31, 769–771 (2006).
[CrossRef]

R. B. Schulz, J. Peter, W. Semmler, C. D’ Andrea, G. Valentini, and R. Cubeddu, “Quantifiability and image quality in non-contact fluorescence tomography,” Proc. SPIE 5859, 58590Z (2005).
[CrossRef]

Soubert, A.

Sun, L.

Q. Tian, Y. Liao, and L. Sun, Engineering Optics (Tsinghua University, 2004).

Tanikawa, Y.

D. Qin, H. Zhao, Y. Tanikawa, and F. Gao, “Experimental determination of optical properties in turbid medium by TCSPC technique,” Proc. SPIE 6434, 64342E (2007).
[CrossRef]

Tian, J.

N. Ren, J. Liang, X. Qu, J. Li, B. Lu, and J. Tian, “GPU-based Monte Carlo simulation for light propagation in complex heterogeneous tissues,” Opt. Express 18, 6811–6823(2010).
[CrossRef] [PubMed]

X. Chen, X. Gao, X. Qu, J. Liang, L. Wang, D. Yang, A. Garofalakis, J. Ripoll, and J. Tian, “A study of photon propagation in free-space based on hybrid radiosity-radiance theorem,” Opt. Express 17, 16266–16280 (2009).
[CrossRef] [PubMed]

J. Tian, J. Bai, X. Yan, S. Bao, Y. Li, W. Liang, and X. Yang, “Multimodality molecular imaging,” IEEE Eng. Med. Biol. Mag. 27, 48–57 (2008).
[CrossRef] [PubMed]

H. Li, J. Tian, F. Zhu, W. X. Cong, L. V. Wang, and G. Wang, “A Mouse Optical Simulation Environment (MOSE) to investigate bioluminescent phenomena in the living mouse with the Monte Carlo method,” Acad. Radiol. 11, 1029–1038(2004).
[CrossRef] [PubMed]

Tian, Q.

Q. Tian, Y. Liao, and L. Sun, Engineering Optics (Tsinghua University, 2004).

Valentini, G.

R. B. Schulz, J. Peter, W. Semmler, C. D’ Andrea, G. Valentini, and R. Cubeddu, “Quantifiability and image quality in non-contact fluorescence tomography,” Proc. SPIE 5859, 58590Z (2005).
[CrossRef]

Wang, G.

H. Li, J. Tian, F. Zhu, W. X. Cong, L. V. Wang, and G. Wang, “A Mouse Optical Simulation Environment (MOSE) to investigate bioluminescent phenomena in the living mouse with the Monte Carlo method,” Acad. Radiol. 11, 1029–1038(2004).
[CrossRef] [PubMed]

Wang, J.

B. Du and J. Wang, Electron Optics (Tsinghua University, 2002).

Wang, L.

Wang, L. V.

V. Ntziachristos, J. Ripoll, L. V. Wang, and R. Weissleder, “Looking and listening to light: the evolution of whole-body photonic imaging,” Nat. Biotechnol. 23, 313–320 (2005).
[CrossRef] [PubMed]

H. Li, J. Tian, F. Zhu, W. X. Cong, L. V. Wang, and G. Wang, “A Mouse Optical Simulation Environment (MOSE) to investigate bioluminescent phenomena in the living mouse with the Monte Carlo method,” Acad. Radiol. 11, 1029–1038(2004).
[CrossRef] [PubMed]

L. V. Wang, S. L. Jacques, and L. Q. Zheng, “MCML-Monte Carlo modeling of photon transport in multi-layered tissues,” Comput. Methods Programs Biomed. 47, 131–146 (1995).
[CrossRef] [PubMed]

Weissleder, R.

V. Ntziachristos, J. Ripoll, L. V. Wang, and R. Weissleder, “Looking and listening to light: the evolution of whole-body photonic imaging,” Nat. Biotechnol. 23, 313–320 (2005).
[CrossRef] [PubMed]

R. Weissleder and V. Ntziachristos, “Shedding light onto live molecular targets,” Nat. Med. 9, 123–128 (2003).
[CrossRef] [PubMed]

Yan, X.

J. Tian, J. Bai, X. Yan, S. Bao, Y. Li, W. Liang, and X. Yang, “Multimodality molecular imaging,” IEEE Eng. Med. Biol. Mag. 27, 48–57 (2008).
[CrossRef] [PubMed]

Yang, D.

Yang, X.

J. Tian, J. Bai, X. Yan, S. Bao, Y. Li, W. Liang, and X. Yang, “Multimodality molecular imaging,” IEEE Eng. Med. Biol. Mag. 27, 48–57 (2008).
[CrossRef] [PubMed]

Zacharakis, G.

Zhang, Y.

Y. Zhang, Applied Optics (Publishing House of Electronics Industry, 2008).
[PubMed]

Zhao, H.

D. Qin, H. Zhao, Y. Tanikawa, and F. Gao, “Experimental determination of optical properties in turbid medium by TCSPC technique,” Proc. SPIE 6434, 64342E (2007).
[CrossRef]

Zheng, L. Q.

L. V. Wang, S. L. Jacques, and L. Q. Zheng, “MCML-Monte Carlo modeling of photon transport in multi-layered tissues,” Comput. Methods Programs Biomed. 47, 131–146 (1995).
[CrossRef] [PubMed]

Zhu, F.

H. Li, J. Tian, F. Zhu, W. X. Cong, L. V. Wang, and G. Wang, “A Mouse Optical Simulation Environment (MOSE) to investigate bioluminescent phenomena in the living mouse with the Monte Carlo method,” Acad. Radiol. 11, 1029–1038(2004).
[CrossRef] [PubMed]

Acad. Radiol. (1)

H. Li, J. Tian, F. Zhu, W. X. Cong, L. V. Wang, and G. Wang, “A Mouse Optical Simulation Environment (MOSE) to investigate bioluminescent phenomena in the living mouse with the Monte Carlo method,” Acad. Radiol. 11, 1029–1038(2004).
[CrossRef] [PubMed]

Appl. Opt. (2)

Comput. Methods Programs Biomed. (1)

L. V. Wang, S. L. Jacques, and L. Q. Zheng, “MCML-Monte Carlo modeling of photon transport in multi-layered tissues,” Comput. Methods Programs Biomed. 47, 131–146 (1995).
[CrossRef] [PubMed]

IEEE Eng. Med. Biol. Mag. (1)

J. Tian, J. Bai, X. Yan, S. Bao, Y. Li, W. Liang, and X. Yang, “Multimodality molecular imaging,” IEEE Eng. Med. Biol. Mag. 27, 48–57 (2008).
[CrossRef] [PubMed]

Int. J. Comput. Vision (1)

M. Aggarwal and N. Ahuja, “A pupil-centric model of image formation,” Int. J. Comput. Vision 48, 195–214 (2002).
[CrossRef]

Inverse Probl. (3)

H. K. Kim and A. H. Hielscher, “A PDE-constrained SQP algorithm for optical tomography based on the frequency-domain equation of radiative transfer,” Inverse Probl. 25, 015010(2009).
[CrossRef]

S. R. Arridge, “Optical tomography in medical imaging,” Inverse Probl. 15, R41–R93 (1999).
[CrossRef]

S. R. Arridge and J. C. Schotland, “Optical tomography: Forward and inverse problems,” Inverse Probl. 25, 123010 (2009).
[CrossRef]

J. Biomed. Opt. (1)

B. W. Rice, M. D. Cable, and M. B. Nelson, “In vivo imaging of light-emitting probes,” J. Biomed. Opt. 6, 432–440 (2001).
[CrossRef] [PubMed]

J. Opt. Soc. Am. A (1)

Mod. Phys. Lett. B (1)

J. Ripoll and V. Ntziachristos, “Imaging scattering media from a distance: theory and applications of non-contact optical tomography,” Mod. Phys. Lett. B 18, 1403–1431 (2004).
[CrossRef]

Nat. Biotechnol. (1)

V. Ntziachristos, J. Ripoll, L. V. Wang, and R. Weissleder, “Looking and listening to light: the evolution of whole-body photonic imaging,” Nat. Biotechnol. 23, 313–320 (2005).
[CrossRef] [PubMed]

Nat. Med. (1)

R. Weissleder and V. Ntziachristos, “Shedding light onto live molecular targets,” Nat. Med. 9, 123–128 (2003).
[CrossRef] [PubMed]

Opt. Express (2)

Opt. Lett. (3)

Phys. Rev. Lett. (1)

J. Ripoll, R. B. Schulz, and V. Ntziachristos, “Free-space propagation of diffuse light: theory and experiment,” Phys. Rev. Lett. 91, 103901 (2003).
[CrossRef] [PubMed]

Proc. SPIE (2)

R. B. Schulz, J. Peter, W. Semmler, C. D’ Andrea, G. Valentini, and R. Cubeddu, “Quantifiability and image quality in non-contact fluorescence tomography,” Proc. SPIE 5859, 58590Z (2005).
[CrossRef]

D. Qin, H. Zhao, Y. Tanikawa, and F. Gao, “Experimental determination of optical properties in turbid medium by TCSPC technique,” Proc. SPIE 6434, 64342E (2007).
[CrossRef]

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[PubMed]

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Figures (9)

Fig. 1
Fig. 1

Schematic diagram of the characteristic of diffuse photons transport in free space emitted from a Lambertian source.

Fig. 2
Fig. 2

Two types of diaphragms in any camera lens: (a) diaphragm located at the front of the lens system and (b) diaphragm located behind the lens system.

Fig. 3
Fig. 3

Schematic diagram of modeling the camera lens diaphragm in the simplification of noncontact optical imaging system.

Fig. 4
Fig. 4

Experimental setup for comparison experiment showing (a) the physical phantom used in the optical imaging experiment, (b) four perspectives for the CCD camera to register escaped photons, (c) the numerical phantom used in the simulation and calculation.

Fig. 5
Fig. 5

Comparison results between the calculated (asterisk lines) and standard flux (solid lines) at the detection position: z d = 0.0 , 2.0, and 4.0 mm . (a)–(c) Comparison of flux between the proposed model and the MC-FSPT model; (d)–(f) comparison of flux between the proposed model and the real experiment. (a) and (d) front perspective, (b) and (e) left perspective, (c) and (f) back perspective.

Fig. 6
Fig. 6

Comparisons between the calculated results of the proposed model (bottom row) and the experimental images on the CCD camera captured with different aperture values (top row) in the left perspective. (a)–(d) captured images at the CCD camera; (e)–(h) calculated results of the proposed model. For (a) and (e), f num = 2.8 ; (b) and (f), f num = 5.6 ; (c) and (g), f num = 11 ; (d) and (h), f num = 22 .

Fig. 7
Fig. 7

Corresponding relationship between the intensity variation and the different aperture values for both the calculated results (asterisk lines) and the experimental data (square lines). (a) Curve for variation of the peak intensity with the different aperture values. (b) Curve for variation of the average intensity with the different aperture values.

Fig. 8
Fig. 8

Corresponding relationship between the pixel distance and the different aperture values for both the calculated results (first column) and the experimental data (second column). (a) Schematic diagram of the definition of pixel distance. (b) Curve for variation of the pixel distance with the different aperture values.

Fig. 9
Fig. 9

Comparisons of flux distribution at the detector plane between the calculation models and the real experiment: (a) experimental results, (b) calculations of the HRRT model, (c) calculations of the proposed mode.

Tables (2)

Tables Icon

Table 1 Error Comparison between the Calculated and the Standard Flux a

Tables Icon

Table 2 Error Comparison of the Proposed Model and the HRRT Model with the Real Experiment a

Equations (10)

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d P ( r d ) = 1 π J n ( r ) ( n s s ) d Ω d S ,
P ( r d ) = 1 π S J n ( r ) ξ ( r , r d ) cos θ s cos θ d | r d r | 2 d A d S ,
D = F f num ,
α ( r , r vd ) = { 1 If ( r vd Ω E ) AND ( s r r vd S = { r } ) , 0 Otherwise,
β ( r , r d ; Ω D ) = { 1 If     s r r vd Ω D , 0 If     s r r vd Ω D = ,
P ( r d ) = 1 π S J n ( r ) ξ ( r , r d ) cos θ s cos θ d | r d r l cos θ s | 2 d A d t 2 d S ,
r d = r vd + l cos θ s .
P ( r d ) = 1 π S J n ( r ) T ( r , r d ) d S ,
T ( r , r d ) = α ( r , r d l cos θ s ) β ( r , r d ; Ω D ) cos θ s cos θ d | r d r l cos θ s | 2 d A d t 2 , r S .
e ¯ = i = 1 N | P cal ( i ) P std ( i ) | / N , ρ = i = 1 N ( P cal ( i ) P ¯ cal ) ( P std ( i ) P ¯ std ) / ( ( N 1 ) σ ( P cal ) σ ( P std ) ) ,

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