F. Riechert, F. Dürr, U. Rohlfing, and U. Lemmer, “Ray-based simulation of the propagation of light with different degrees coherence through complex optical systems,” Appl. Opt. 48, 1527–1534 (2009).

[Crossref]
[PubMed]

S. P. Fang, M. Komori, A. Kubo, and X. S. Mei, “Ray tracing method for optical system of interferometry measurement used for form deviation of precise complex surface of machine parts,” Chin. J. Mech. Eng. 45(2), 170–177 (2009), in Chinese.

[Crossref]

S. P. Fang, M. Komori, A. Kubo, and X. S. Mei, “Precision simulation method for images of interference fringe pattern in complex optical system,” Chin. J. Mech. Eng. 45(1), 244–252 (2009), in Chinese.

[Crossref]

J. E. Klein, “Demystifying the sequential ray tracing algorithm,” Proc. SPIE 4769, 67–74 (2002).

[Crossref]

Norbert Lindlein, “Simulation of micro-optical systems including microlens arrays,” J. Opt. A Pure Appl. Opt. 4, S1–S9 (2002).

[Crossref]

A. Cordero-Dávila, J. Díaz-Anzures, and V. Cabrera-Peláez, “Algorithm for the simulation of Ronchigrams of arbitrary optical systems and Ronchi grids in generalized coordinates,” Appl. Opt. 41, 3866–3873 (2002).

[Crossref]
[PubMed]

J. E. Klein, “Challenges and problems in non-sequential ray tracing,” Proc. SPIE 4442, 60–66 (2001).

[Crossref]

S. P. Fang, H. Fujio, A. Kubo, M. Toya, Y. Suzuki, Y. Saitoh, and M. Suzuki, “New optical system for reducing the interference fringe density in laser interferometric measurement of tooth flank form of a gear,” JSME Int. J. Ser. C 43(2), 455–463 (2000).

S. Fang, T. Nakai, A. Kubo, H. Fujio, Y. Saitoh, and M. Suzuki, “Fringe density reduction of relative phase difference in laser interferometry measurement of gear tooth flank,” Trans. Jpn. Soc. Mech. Eng. C 64, 1421–1427 (1998), in Japanese.

[Crossref]

N. Lindlein, F. Simon, and Johannes Schwider, “Simulation of micro-optical arrays systems with RAYTRACE,” Opt. Eng. 37, 1809–1816 (1998).

[Crossref]

H. Fujio, A. Kubo, S. P. Fang, K. Oyama, T. Yatagai, Y. Saitoh, and M. Suzuki, “Measurement of gear tooth form deviation by laser interferometry using CCD image sensor,” Trans. Jpn. Soc. Mech. Eng. C 62, 2422–2430 (1996), in Japanese.

[Crossref]

Nigel G. Douglas, Andrew R. Jones, and Frans J. van Hoesel, “Ray-based simulation of an optical interferometer,” J. Opt. Soc. Am. A 12, 124–131 (1995).

[Crossref]

S. Fang, A. Kubo, H. Fujio, K. Oyama, Y. Saitoh, and M. Suzuki, “Phase processing method of interferometry measurement for form deviation of the surface of machine parts,” Trans. Jpn. Soc. Mech. Eng. C 61, 106–114 (1995), in Japanese.

[Crossref]

J. R. Colbourne, The Geometry of Involute Gears (Springer-Verlag, 1987).

[Crossref]

S. Fang, T. Nakai, A. Kubo, H. Fujio, Y. Saitoh, and M. Suzuki, “Fringe density reduction of relative phase difference in laser interferometry measurement of gear tooth flank,” Trans. Jpn. Soc. Mech. Eng. C 64, 1421–1427 (1998), in Japanese.

[Crossref]

S. Fang, A. Kubo, H. Fujio, K. Oyama, Y. Saitoh, and M. Suzuki, “Phase processing method of interferometry measurement for form deviation of the surface of machine parts,” Trans. Jpn. Soc. Mech. Eng. C 61, 106–114 (1995), in Japanese.

[Crossref]

S. Fang, A. Kubo, H. Fujio, K. Oyama, Y. Saitoh, and M. Suzuki, “Digital phase data processing method for laser interferometry measurement of gear tooth flank,” in Proceedings of VDI International Conference on Gears (VDI Verlag, 1996), Vol. 1230, pp. 1111–1123.

S. P. Fang, M. Komori, A. Kubo, and X. S. Mei, “Precision simulation method for images of interference fringe pattern in complex optical system,” Chin. J. Mech. Eng. 45(1), 244–252 (2009), in Chinese.

[Crossref]

S. P. Fang, M. Komori, A. Kubo, and X. S. Mei, “Ray tracing method for optical system of interferometry measurement used for form deviation of precise complex surface of machine parts,” Chin. J. Mech. Eng. 45(2), 170–177 (2009), in Chinese.

[Crossref]

S. P. Fang, H. Fujio, A. Kubo, M. Toya, Y. Suzuki, Y. Saitoh, and M. Suzuki, “New optical system for reducing the interference fringe density in laser interferometric measurement of tooth flank form of a gear,” JSME Int. J. Ser. C 43(2), 455–463 (2000).

H. Fujio, A. Kubo, S. P. Fang, K. Oyama, T. Yatagai, Y. Saitoh, and M. Suzuki, “Measurement of gear tooth form deviation by laser interferometry using CCD image sensor,” Trans. Jpn. Soc. Mech. Eng. C 62, 2422–2430 (1996), in Japanese.

[Crossref]

S. P. Fang, H. Fujio, A. Kubo, M. Toya, Y. Suzuki, Y. Saitoh, and M. Suzuki, “New optical system for reducing the interference fringe density in laser interferometric measurement of tooth flank form of a gear,” JSME Int. J. Ser. C 43(2), 455–463 (2000).

S. Fang, T. Nakai, A. Kubo, H. Fujio, Y. Saitoh, and M. Suzuki, “Fringe density reduction of relative phase difference in laser interferometry measurement of gear tooth flank,” Trans. Jpn. Soc. Mech. Eng. C 64, 1421–1427 (1998), in Japanese.

[Crossref]

H. Fujio, A. Kubo, S. P. Fang, K. Oyama, T. Yatagai, Y. Saitoh, and M. Suzuki, “Measurement of gear tooth form deviation by laser interferometry using CCD image sensor,” Trans. Jpn. Soc. Mech. Eng. C 62, 2422–2430 (1996), in Japanese.

[Crossref]

S. Fang, A. Kubo, H. Fujio, K. Oyama, Y. Saitoh, and M. Suzuki, “Phase processing method of interferometry measurement for form deviation of the surface of machine parts,” Trans. Jpn. Soc. Mech. Eng. C 61, 106–114 (1995), in Japanese.

[Crossref]

S. Fang, A. Kubo, H. Fujio, K. Oyama, Y. Saitoh, and M. Suzuki, “Digital phase data processing method for laser interferometry measurement of gear tooth flank,” in Proceedings of VDI International Conference on Gears (VDI Verlag, 1996), Vol. 1230, pp. 1111–1123.

J. E. Klein, “Demystifying the sequential ray tracing algorithm,” Proc. SPIE 4769, 67–74 (2002).

[Crossref]

J. E. Klein, “Challenges and problems in non-sequential ray tracing,” Proc. SPIE 4442, 60–66 (2001).

[Crossref]

S. P. Fang, M. Komori, A. Kubo, and X. S. Mei, “Ray tracing method for optical system of interferometry measurement used for form deviation of precise complex surface of machine parts,” Chin. J. Mech. Eng. 45(2), 170–177 (2009), in Chinese.

[Crossref]

S. P. Fang, M. Komori, A. Kubo, and X. S. Mei, “Precision simulation method for images of interference fringe pattern in complex optical system,” Chin. J. Mech. Eng. 45(1), 244–252 (2009), in Chinese.

[Crossref]

S. P. Fang, M. Komori, A. Kubo, and X. S. Mei, “Precision simulation method for images of interference fringe pattern in complex optical system,” Chin. J. Mech. Eng. 45(1), 244–252 (2009), in Chinese.

[Crossref]

S. P. Fang, M. Komori, A. Kubo, and X. S. Mei, “Ray tracing method for optical system of interferometry measurement used for form deviation of precise complex surface of machine parts,” Chin. J. Mech. Eng. 45(2), 170–177 (2009), in Chinese.

[Crossref]

S. P. Fang, H. Fujio, A. Kubo, M. Toya, Y. Suzuki, Y. Saitoh, and M. Suzuki, “New optical system for reducing the interference fringe density in laser interferometric measurement of tooth flank form of a gear,” JSME Int. J. Ser. C 43(2), 455–463 (2000).

S. Fang, T. Nakai, A. Kubo, H. Fujio, Y. Saitoh, and M. Suzuki, “Fringe density reduction of relative phase difference in laser interferometry measurement of gear tooth flank,” Trans. Jpn. Soc. Mech. Eng. C 64, 1421–1427 (1998), in Japanese.

[Crossref]

H. Fujio, A. Kubo, S. P. Fang, K. Oyama, T. Yatagai, Y. Saitoh, and M. Suzuki, “Measurement of gear tooth form deviation by laser interferometry using CCD image sensor,” Trans. Jpn. Soc. Mech. Eng. C 62, 2422–2430 (1996), in Japanese.

[Crossref]

S. Fang, A. Kubo, H. Fujio, K. Oyama, Y. Saitoh, and M. Suzuki, “Phase processing method of interferometry measurement for form deviation of the surface of machine parts,” Trans. Jpn. Soc. Mech. Eng. C 61, 106–114 (1995), in Japanese.

[Crossref]

S. Fang, A. Kubo, H. Fujio, K. Oyama, Y. Saitoh, and M. Suzuki, “Digital phase data processing method for laser interferometry measurement of gear tooth flank,” in Proceedings of VDI International Conference on Gears (VDI Verlag, 1996), Vol. 1230, pp. 1111–1123.

N. Lindlein, F. Simon, and Johannes Schwider, “Simulation of micro-optical arrays systems with RAYTRACE,” Opt. Eng. 37, 1809–1816 (1998).

[Crossref]

Norbert Lindlein, “Simulation of micro-optical systems including microlens arrays,” J. Opt. A Pure Appl. Opt. 4, S1–S9 (2002).

[Crossref]

S. P. Fang, M. Komori, A. Kubo, and X. S. Mei, “Ray tracing method for optical system of interferometry measurement used for form deviation of precise complex surface of machine parts,” Chin. J. Mech. Eng. 45(2), 170–177 (2009), in Chinese.

[Crossref]

S. P. Fang, M. Komori, A. Kubo, and X. S. Mei, “Precision simulation method for images of interference fringe pattern in complex optical system,” Chin. J. Mech. Eng. 45(1), 244–252 (2009), in Chinese.

[Crossref]

S. Fang, T. Nakai, A. Kubo, H. Fujio, Y. Saitoh, and M. Suzuki, “Fringe density reduction of relative phase difference in laser interferometry measurement of gear tooth flank,” Trans. Jpn. Soc. Mech. Eng. C 64, 1421–1427 (1998), in Japanese.

[Crossref]

H. Fujio, A. Kubo, S. P. Fang, K. Oyama, T. Yatagai, Y. Saitoh, and M. Suzuki, “Measurement of gear tooth form deviation by laser interferometry using CCD image sensor,” Trans. Jpn. Soc. Mech. Eng. C 62, 2422–2430 (1996), in Japanese.

[Crossref]

S. Fang, A. Kubo, H. Fujio, K. Oyama, Y. Saitoh, and M. Suzuki, “Phase processing method of interferometry measurement for form deviation of the surface of machine parts,” Trans. Jpn. Soc. Mech. Eng. C 61, 106–114 (1995), in Japanese.

[Crossref]

S. Fang, A. Kubo, H. Fujio, K. Oyama, Y. Saitoh, and M. Suzuki, “Digital phase data processing method for laser interferometry measurement of gear tooth flank,” in Proceedings of VDI International Conference on Gears (VDI Verlag, 1996), Vol. 1230, pp. 1111–1123.

S. P. Fang, H. Fujio, A. Kubo, M. Toya, Y. Suzuki, Y. Saitoh, and M. Suzuki, “New optical system for reducing the interference fringe density in laser interferometric measurement of tooth flank form of a gear,” JSME Int. J. Ser. C 43(2), 455–463 (2000).

S. Fang, T. Nakai, A. Kubo, H. Fujio, Y. Saitoh, and M. Suzuki, “Fringe density reduction of relative phase difference in laser interferometry measurement of gear tooth flank,” Trans. Jpn. Soc. Mech. Eng. C 64, 1421–1427 (1998), in Japanese.

[Crossref]

H. Fujio, A. Kubo, S. P. Fang, K. Oyama, T. Yatagai, Y. Saitoh, and M. Suzuki, “Measurement of gear tooth form deviation by laser interferometry using CCD image sensor,” Trans. Jpn. Soc. Mech. Eng. C 62, 2422–2430 (1996), in Japanese.

[Crossref]

S. Fang, A. Kubo, H. Fujio, K. Oyama, Y. Saitoh, and M. Suzuki, “Phase processing method of interferometry measurement for form deviation of the surface of machine parts,” Trans. Jpn. Soc. Mech. Eng. C 61, 106–114 (1995), in Japanese.

[Crossref]

S. Fang, A. Kubo, H. Fujio, K. Oyama, Y. Saitoh, and M. Suzuki, “Digital phase data processing method for laser interferometry measurement of gear tooth flank,” in Proceedings of VDI International Conference on Gears (VDI Verlag, 1996), Vol. 1230, pp. 1111–1123.

N. Lindlein, F. Simon, and Johannes Schwider, “Simulation of micro-optical arrays systems with RAYTRACE,” Opt. Eng. 37, 1809–1816 (1998).

[Crossref]

N. Lindlein, F. Simon, and Johannes Schwider, “Simulation of micro-optical arrays systems with RAYTRACE,” Opt. Eng. 37, 1809–1816 (1998).

[Crossref]

S. P. Fang, H. Fujio, A. Kubo, M. Toya, Y. Suzuki, Y. Saitoh, and M. Suzuki, “New optical system for reducing the interference fringe density in laser interferometric measurement of tooth flank form of a gear,” JSME Int. J. Ser. C 43(2), 455–463 (2000).

S. Fang, T. Nakai, A. Kubo, H. Fujio, Y. Saitoh, and M. Suzuki, “Fringe density reduction of relative phase difference in laser interferometry measurement of gear tooth flank,” Trans. Jpn. Soc. Mech. Eng. C 64, 1421–1427 (1998), in Japanese.

[Crossref]

H. Fujio, A. Kubo, S. P. Fang, K. Oyama, T. Yatagai, Y. Saitoh, and M. Suzuki, “Measurement of gear tooth form deviation by laser interferometry using CCD image sensor,” Trans. Jpn. Soc. Mech. Eng. C 62, 2422–2430 (1996), in Japanese.

[Crossref]

S. Fang, A. Kubo, H. Fujio, K. Oyama, Y. Saitoh, and M. Suzuki, “Phase processing method of interferometry measurement for form deviation of the surface of machine parts,” Trans. Jpn. Soc. Mech. Eng. C 61, 106–114 (1995), in Japanese.

[Crossref]

S. Fang, A. Kubo, H. Fujio, K. Oyama, Y. Saitoh, and M. Suzuki, “Digital phase data processing method for laser interferometry measurement of gear tooth flank,” in Proceedings of VDI International Conference on Gears (VDI Verlag, 1996), Vol. 1230, pp. 1111–1123.

S. P. Fang, H. Fujio, A. Kubo, M. Toya, Y. Suzuki, Y. Saitoh, and M. Suzuki, “New optical system for reducing the interference fringe density in laser interferometric measurement of tooth flank form of a gear,” JSME Int. J. Ser. C 43(2), 455–463 (2000).

S. P. Fang, H. Fujio, A. Kubo, M. Toya, Y. Suzuki, Y. Saitoh, and M. Suzuki, “New optical system for reducing the interference fringe density in laser interferometric measurement of tooth flank form of a gear,” JSME Int. J. Ser. C 43(2), 455–463 (2000).

H. Fujio, A. Kubo, S. P. Fang, K. Oyama, T. Yatagai, Y. Saitoh, and M. Suzuki, “Measurement of gear tooth form deviation by laser interferometry using CCD image sensor,” Trans. Jpn. Soc. Mech. Eng. C 62, 2422–2430 (1996), in Japanese.

[Crossref]

A. Cordero-Dávila, J. Díaz-Anzures, and V. Cabrera-Peláez, “Algorithm for the simulation of Ronchigrams of arbitrary optical systems and Ronchi grids in generalized coordinates,” Appl. Opt. 41, 3866–3873 (2002).

[Crossref]
[PubMed]

F. Riechert, F. Dürr, U. Rohlfing, and U. Lemmer, “Ray-based simulation of the propagation of light with different degrees coherence through complex optical systems,” Appl. Opt. 48, 1527–1534 (2009).

[Crossref]
[PubMed]

M. N. Akram, “Simulation and control of narcissus phenomenon using nonsequential ray tracing. 1. Staring camera in 3–5 μm waveband,” Appl. Opt. 49, 964–975 (2010).

[Crossref]
[PubMed]

S. P. Fang, M. Komori, A. Kubo, and X. S. Mei, “Ray tracing method for optical system of interferometry measurement used for form deviation of precise complex surface of machine parts,” Chin. J. Mech. Eng. 45(2), 170–177 (2009), in Chinese.

[Crossref]

S. P. Fang, M. Komori, A. Kubo, and X. S. Mei, “Precision simulation method for images of interference fringe pattern in complex optical system,” Chin. J. Mech. Eng. 45(1), 244–252 (2009), in Chinese.

[Crossref]

Norbert Lindlein, “Simulation of micro-optical systems including microlens arrays,” J. Opt. A Pure Appl. Opt. 4, S1–S9 (2002).

[Crossref]

S. P. Fang, H. Fujio, A. Kubo, M. Toya, Y. Suzuki, Y. Saitoh, and M. Suzuki, “New optical system for reducing the interference fringe density in laser interferometric measurement of tooth flank form of a gear,” JSME Int. J. Ser. C 43(2), 455–463 (2000).

N. Lindlein, F. Simon, and Johannes Schwider, “Simulation of micro-optical arrays systems with RAYTRACE,” Opt. Eng. 37, 1809–1816 (1998).

[Crossref]

J. E. Klein, “Challenges and problems in non-sequential ray tracing,” Proc. SPIE 4442, 60–66 (2001).

[Crossref]

J. E. Klein, “Demystifying the sequential ray tracing algorithm,” Proc. SPIE 4769, 67–74 (2002).

[Crossref]

S. Fang, A. Kubo, H. Fujio, K. Oyama, Y. Saitoh, and M. Suzuki, “Phase processing method of interferometry measurement for form deviation of the surface of machine parts,” Trans. Jpn. Soc. Mech. Eng. C 61, 106–114 (1995), in Japanese.

[Crossref]

S. Fang, T. Nakai, A. Kubo, H. Fujio, Y. Saitoh, and M. Suzuki, “Fringe density reduction of relative phase difference in laser interferometry measurement of gear tooth flank,” Trans. Jpn. Soc. Mech. Eng. C 64, 1421–1427 (1998), in Japanese.

[Crossref]

H. Fujio, A. Kubo, S. P. Fang, K. Oyama, T. Yatagai, Y. Saitoh, and M. Suzuki, “Measurement of gear tooth form deviation by laser interferometry using CCD image sensor,” Trans. Jpn. Soc. Mech. Eng. C 62, 2422–2430 (1996), in Japanese.

[Crossref]

http://en.wikipedia.org/wiki/Involute_gear.

J. R. Colbourne, The Geometry of Involute Gears (Springer-Verlag, 1987).

[Crossref]

http://en.wikipedia.org/wiki/Involute.

S. Fang, A. Kubo, H. Fujio, K. Oyama, Y. Saitoh, and M. Suzuki, “Digital phase data processing method for laser interferometry measurement of gear tooth flank,” in Proceedings of VDI International Conference on Gears (VDI Verlag, 1996), Vol. 1230, pp. 1111–1123.