Abstract

An improved method of backward ray tracing is proposed according to the theory of geometrical optics and thermal radiation heat transfer. The accuracy is essentially raised comparing to the traditional backward ray tracing because ray orders and weight factors are taken into account and the process is designed as sequential and recurring steps to trace and calculate different order stray lights. Meanwhile, it needs very small computation comparing to forward ray tracing because irrelevant surfaces and rays are excluded from the tracing. The effectiveness was verified in the stray radiation analysis for a cryogenic infrared (IR) imaging system, as the results coincided with the actual stray radiation irradiance distributions in the real images. The computation amount was compared with that of forward ray tracing in the narcissus calculation for another cryogenic IR imaging system, it was found that to produce the same accuracy result, the computation of the improved backward ray tracing is far smaller than that of forward ray tracing by at least 2 orders of magnitude.

© 2013 Optical Society of America

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References

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  1. J. W. Howard and I. R. Abel, “Narcissus: reflections on retro-reflections in thermal imaging systems,” Appl. Opt. 21, 3393–3397 (1982).
    [CrossRef]
  2. J. L. Rayces and L. Lebich, “Exact ray-tracing computation of narcissus equivalent temperature difference in scanning thermal imagers,” Proc. SPIE 1752, 325–332 (1992).
    [CrossRef]
  3. K. Lu and S. J. Dobson, “Accurate calculation of Narcissus signatures by using finite ray tracing,” Appl. Opt. 36, 6393–6398 (1997).
    [CrossRef]
  4. M. N. Akram, “Simulation and control of narcissus phenomenon using nonsequential ray tracing. II. Line-scan camera in 7–11 μm waveband,” Appl. Opt. 49, 1185–1195(2010).
    [CrossRef]
  5. F.-Y. He, J.-C. Cui, S.-L. Feng, and X. Zhang, “Narcissus analysis for cooled staring IR system,” Proc. SPIE 6722, 67224N (2007).
    [CrossRef]
  6. Optical Research Associates, “Narcissus analysis,” in Code V Reference Manual (Optical Research Associates, 2004), pp. 39–49.
  7. C. R. Boshuizen, M. G. Grimminck, H. Kjeldsen, and A. G. Monger, “MONS space telescope, part 2: analysis of very high stray-light rejection,” Opt. Eng. 47, 013001 (2008).
    [CrossRef]
  8. J. L. Stauder, “Stray light design and analysis of the Wide-Field Infrared Explorer,” Proc. SPIE 3122, 35–44(1998).
    [CrossRef]
  9. S. M. Pompea, I. E. Mentzell, and W. A. Siegmund, “A stray light analysis of the 2.5 meter telescope for the sloan digital sky survey,” Proc. SPIE 1793, 173–182 (1992).
    [CrossRef]
  10. J.-X. Niu, S. Shi, and R.-K. Zhou, “Analysis to stray radiation of infrared detecting system,” Proc. SPIE8193, 81931H (2011).
  11. R. Siegel and J. R. Howell, Thermal Radiation Heat Transfer (Academic, 1972).
  12. W. J. Smith, “Radiometry and photometry,” in Modern Optical Engineering (Academic, 2000), pp. 19–249.
  13. M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light (Academic, 2005).
  14. FLIR, The Ultimate Infrared Handbook for R&D Professionals (Academic, 2009).
  15. M. E. Thomas, R. I. Joseph, W. J. Tropf, and A. M. Brown, “A general BRDF/BSDF model including out-of-plane dependence,” Proc. SPIE 7792, 1–12 (2010).
    [CrossRef]
  16. M. E. Thomas, D. W. Blodgett, and D. V. Hahn, “Analysis and representation of BSDF and BRDF measurements,” Proc. SPIE 5192, 158–167 (2003).
    [CrossRef]
  17. S. M. Pompea, “Assessment of black and spectrally selective surfaces for stray light reduction in telescope systems,” Proc. SPIE 7739, 1–11 (2010).
    [CrossRef]
  18. J. E. Harvey, S. Schröder, N. Choi, and A. Duparré, “Total integrated scatter from surfaces with arbitrary roughness, correlation widths, and incident angles,” Opt. Eng. 51, 013402 (2012).
    [CrossRef]

2012 (1)

J. E. Harvey, S. Schröder, N. Choi, and A. Duparré, “Total integrated scatter from surfaces with arbitrary roughness, correlation widths, and incident angles,” Opt. Eng. 51, 013402 (2012).
[CrossRef]

2010 (3)

S. M. Pompea, “Assessment of black and spectrally selective surfaces for stray light reduction in telescope systems,” Proc. SPIE 7739, 1–11 (2010).
[CrossRef]

M. N. Akram, “Simulation and control of narcissus phenomenon using nonsequential ray tracing. II. Line-scan camera in 7–11 μm waveband,” Appl. Opt. 49, 1185–1195(2010).
[CrossRef]

M. E. Thomas, R. I. Joseph, W. J. Tropf, and A. M. Brown, “A general BRDF/BSDF model including out-of-plane dependence,” Proc. SPIE 7792, 1–12 (2010).
[CrossRef]

2008 (1)

C. R. Boshuizen, M. G. Grimminck, H. Kjeldsen, and A. G. Monger, “MONS space telescope, part 2: analysis of very high stray-light rejection,” Opt. Eng. 47, 013001 (2008).
[CrossRef]

2007 (1)

F.-Y. He, J.-C. Cui, S.-L. Feng, and X. Zhang, “Narcissus analysis for cooled staring IR system,” Proc. SPIE 6722, 67224N (2007).
[CrossRef]

2003 (1)

M. E. Thomas, D. W. Blodgett, and D. V. Hahn, “Analysis and representation of BSDF and BRDF measurements,” Proc. SPIE 5192, 158–167 (2003).
[CrossRef]

1998 (1)

J. L. Stauder, “Stray light design and analysis of the Wide-Field Infrared Explorer,” Proc. SPIE 3122, 35–44(1998).
[CrossRef]

1997 (1)

K. Lu and S. J. Dobson, “Accurate calculation of Narcissus signatures by using finite ray tracing,” Appl. Opt. 36, 6393–6398 (1997).
[CrossRef]

1992 (2)

S. M. Pompea, I. E. Mentzell, and W. A. Siegmund, “A stray light analysis of the 2.5 meter telescope for the sloan digital sky survey,” Proc. SPIE 1793, 173–182 (1992).
[CrossRef]

J. L. Rayces and L. Lebich, “Exact ray-tracing computation of narcissus equivalent temperature difference in scanning thermal imagers,” Proc. SPIE 1752, 325–332 (1992).
[CrossRef]

1982 (1)

J. W. Howard and I. R. Abel, “Narcissus: reflections on retro-reflections in thermal imaging systems,” Appl. Opt. 21, 3393–3397 (1982).
[CrossRef]

Abel, I. R.

J. W. Howard and I. R. Abel, “Narcissus: reflections on retro-reflections in thermal imaging systems,” Appl. Opt. 21, 3393–3397 (1982).
[CrossRef]

Akram, M. N.

M. N. Akram, “Simulation and control of narcissus phenomenon using nonsequential ray tracing. II. Line-scan camera in 7–11 μm waveband,” Appl. Opt. 49, 1185–1195(2010).
[CrossRef]

Blodgett, D. W.

M. E. Thomas, D. W. Blodgett, and D. V. Hahn, “Analysis and representation of BSDF and BRDF measurements,” Proc. SPIE 5192, 158–167 (2003).
[CrossRef]

Born, M.

M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light (Academic, 2005).

Boshuizen, C. R.

C. R. Boshuizen, M. G. Grimminck, H. Kjeldsen, and A. G. Monger, “MONS space telescope, part 2: analysis of very high stray-light rejection,” Opt. Eng. 47, 013001 (2008).
[CrossRef]

Brown, A. M.

M. E. Thomas, R. I. Joseph, W. J. Tropf, and A. M. Brown, “A general BRDF/BSDF model including out-of-plane dependence,” Proc. SPIE 7792, 1–12 (2010).
[CrossRef]

Choi, N.

J. E. Harvey, S. Schröder, N. Choi, and A. Duparré, “Total integrated scatter from surfaces with arbitrary roughness, correlation widths, and incident angles,” Opt. Eng. 51, 013402 (2012).
[CrossRef]

Cui, J.-C.

F.-Y. He, J.-C. Cui, S.-L. Feng, and X. Zhang, “Narcissus analysis for cooled staring IR system,” Proc. SPIE 6722, 67224N (2007).
[CrossRef]

Dobson, S. J.

K. Lu and S. J. Dobson, “Accurate calculation of Narcissus signatures by using finite ray tracing,” Appl. Opt. 36, 6393–6398 (1997).
[CrossRef]

Duparré, A.

J. E. Harvey, S. Schröder, N. Choi, and A. Duparré, “Total integrated scatter from surfaces with arbitrary roughness, correlation widths, and incident angles,” Opt. Eng. 51, 013402 (2012).
[CrossRef]

Feng, S.-L.

F.-Y. He, J.-C. Cui, S.-L. Feng, and X. Zhang, “Narcissus analysis for cooled staring IR system,” Proc. SPIE 6722, 67224N (2007).
[CrossRef]

Grimminck, M. G.

C. R. Boshuizen, M. G. Grimminck, H. Kjeldsen, and A. G. Monger, “MONS space telescope, part 2: analysis of very high stray-light rejection,” Opt. Eng. 47, 013001 (2008).
[CrossRef]

Hahn, D. V.

M. E. Thomas, D. W. Blodgett, and D. V. Hahn, “Analysis and representation of BSDF and BRDF measurements,” Proc. SPIE 5192, 158–167 (2003).
[CrossRef]

Harvey, J. E.

J. E. Harvey, S. Schröder, N. Choi, and A. Duparré, “Total integrated scatter from surfaces with arbitrary roughness, correlation widths, and incident angles,” Opt. Eng. 51, 013402 (2012).
[CrossRef]

He, F.-Y.

F.-Y. He, J.-C. Cui, S.-L. Feng, and X. Zhang, “Narcissus analysis for cooled staring IR system,” Proc. SPIE 6722, 67224N (2007).
[CrossRef]

Howard, J. W.

J. W. Howard and I. R. Abel, “Narcissus: reflections on retro-reflections in thermal imaging systems,” Appl. Opt. 21, 3393–3397 (1982).
[CrossRef]

Howell, J. R.

R. Siegel and J. R. Howell, Thermal Radiation Heat Transfer (Academic, 1972).

Joseph, R. I.

M. E. Thomas, R. I. Joseph, W. J. Tropf, and A. M. Brown, “A general BRDF/BSDF model including out-of-plane dependence,” Proc. SPIE 7792, 1–12 (2010).
[CrossRef]

Kjeldsen, H.

C. R. Boshuizen, M. G. Grimminck, H. Kjeldsen, and A. G. Monger, “MONS space telescope, part 2: analysis of very high stray-light rejection,” Opt. Eng. 47, 013001 (2008).
[CrossRef]

Lebich, L.

J. L. Rayces and L. Lebich, “Exact ray-tracing computation of narcissus equivalent temperature difference in scanning thermal imagers,” Proc. SPIE 1752, 325–332 (1992).
[CrossRef]

Lu, K.

K. Lu and S. J. Dobson, “Accurate calculation of Narcissus signatures by using finite ray tracing,” Appl. Opt. 36, 6393–6398 (1997).
[CrossRef]

Mentzell, I. E.

S. M. Pompea, I. E. Mentzell, and W. A. Siegmund, “A stray light analysis of the 2.5 meter telescope for the sloan digital sky survey,” Proc. SPIE 1793, 173–182 (1992).
[CrossRef]

Monger, A. G.

C. R. Boshuizen, M. G. Grimminck, H. Kjeldsen, and A. G. Monger, “MONS space telescope, part 2: analysis of very high stray-light rejection,” Opt. Eng. 47, 013001 (2008).
[CrossRef]

Niu, J.-X.

J.-X. Niu, S. Shi, and R.-K. Zhou, “Analysis to stray radiation of infrared detecting system,” Proc. SPIE8193, 81931H (2011).

Pompea, S. M.

S. M. Pompea, “Assessment of black and spectrally selective surfaces for stray light reduction in telescope systems,” Proc. SPIE 7739, 1–11 (2010).
[CrossRef]

S. M. Pompea, I. E. Mentzell, and W. A. Siegmund, “A stray light analysis of the 2.5 meter telescope for the sloan digital sky survey,” Proc. SPIE 1793, 173–182 (1992).
[CrossRef]

Rayces, J. L.

J. L. Rayces and L. Lebich, “Exact ray-tracing computation of narcissus equivalent temperature difference in scanning thermal imagers,” Proc. SPIE 1752, 325–332 (1992).
[CrossRef]

Schröder, S.

J. E. Harvey, S. Schröder, N. Choi, and A. Duparré, “Total integrated scatter from surfaces with arbitrary roughness, correlation widths, and incident angles,” Opt. Eng. 51, 013402 (2012).
[CrossRef]

Shi, S.

J.-X. Niu, S. Shi, and R.-K. Zhou, “Analysis to stray radiation of infrared detecting system,” Proc. SPIE8193, 81931H (2011).

Siegel, R.

R. Siegel and J. R. Howell, Thermal Radiation Heat Transfer (Academic, 1972).

Siegmund, W. A.

S. M. Pompea, I. E. Mentzell, and W. A. Siegmund, “A stray light analysis of the 2.5 meter telescope for the sloan digital sky survey,” Proc. SPIE 1793, 173–182 (1992).
[CrossRef]

Smith, W. J.

W. J. Smith, “Radiometry and photometry,” in Modern Optical Engineering (Academic, 2000), pp. 19–249.

Stauder, J. L.

J. L. Stauder, “Stray light design and analysis of the Wide-Field Infrared Explorer,” Proc. SPIE 3122, 35–44(1998).
[CrossRef]

Thomas, M. E.

M. E. Thomas, R. I. Joseph, W. J. Tropf, and A. M. Brown, “A general BRDF/BSDF model including out-of-plane dependence,” Proc. SPIE 7792, 1–12 (2010).
[CrossRef]

M. E. Thomas, D. W. Blodgett, and D. V. Hahn, “Analysis and representation of BSDF and BRDF measurements,” Proc. SPIE 5192, 158–167 (2003).
[CrossRef]

Tropf, W. J.

M. E. Thomas, R. I. Joseph, W. J. Tropf, and A. M. Brown, “A general BRDF/BSDF model including out-of-plane dependence,” Proc. SPIE 7792, 1–12 (2010).
[CrossRef]

Wolf, E.

M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light (Academic, 2005).

Zhang, X.

F.-Y. He, J.-C. Cui, S.-L. Feng, and X. Zhang, “Narcissus analysis for cooled staring IR system,” Proc. SPIE 6722, 67224N (2007).
[CrossRef]

Zhou, R.-K.

J.-X. Niu, S. Shi, and R.-K. Zhou, “Analysis to stray radiation of infrared detecting system,” Proc. SPIE8193, 81931H (2011).

Appl. Opt. (3)

K. Lu and S. J. Dobson, “Accurate calculation of Narcissus signatures by using finite ray tracing,” Appl. Opt. 36, 6393–6398 (1997).
[CrossRef]

M. N. Akram, “Simulation and control of narcissus phenomenon using nonsequential ray tracing. II. Line-scan camera in 7–11 μm waveband,” Appl. Opt. 49, 1185–1195(2010).
[CrossRef]

J. W. Howard and I. R. Abel, “Narcissus: reflections on retro-reflections in thermal imaging systems,” Appl. Opt. 21, 3393–3397 (1982).
[CrossRef]

Opt. Eng. (2)

C. R. Boshuizen, M. G. Grimminck, H. Kjeldsen, and A. G. Monger, “MONS space telescope, part 2: analysis of very high stray-light rejection,” Opt. Eng. 47, 013001 (2008).
[CrossRef]

J. E. Harvey, S. Schröder, N. Choi, and A. Duparré, “Total integrated scatter from surfaces with arbitrary roughness, correlation widths, and incident angles,” Opt. Eng. 51, 013402 (2012).
[CrossRef]

Proc. SPIE (7)

J. L. Stauder, “Stray light design and analysis of the Wide-Field Infrared Explorer,” Proc. SPIE 3122, 35–44(1998).
[CrossRef]

S. M. Pompea, I. E. Mentzell, and W. A. Siegmund, “A stray light analysis of the 2.5 meter telescope for the sloan digital sky survey,” Proc. SPIE 1793, 173–182 (1992).
[CrossRef]

J. L. Rayces and L. Lebich, “Exact ray-tracing computation of narcissus equivalent temperature difference in scanning thermal imagers,” Proc. SPIE 1752, 325–332 (1992).
[CrossRef]

M. E. Thomas, R. I. Joseph, W. J. Tropf, and A. M. Brown, “A general BRDF/BSDF model including out-of-plane dependence,” Proc. SPIE 7792, 1–12 (2010).
[CrossRef]

M. E. Thomas, D. W. Blodgett, and D. V. Hahn, “Analysis and representation of BSDF and BRDF measurements,” Proc. SPIE 5192, 158–167 (2003).
[CrossRef]

S. M. Pompea, “Assessment of black and spectrally selective surfaces for stray light reduction in telescope systems,” Proc. SPIE 7739, 1–11 (2010).
[CrossRef]

F.-Y. He, J.-C. Cui, S.-L. Feng, and X. Zhang, “Narcissus analysis for cooled staring IR system,” Proc. SPIE 6722, 67224N (2007).
[CrossRef]

Other (6)

Optical Research Associates, “Narcissus analysis,” in Code V Reference Manual (Optical Research Associates, 2004), pp. 39–49.

J.-X. Niu, S. Shi, and R.-K. Zhou, “Analysis to stray radiation of infrared detecting system,” Proc. SPIE8193, 81931H (2011).

R. Siegel and J. R. Howell, Thermal Radiation Heat Transfer (Academic, 1972).

W. J. Smith, “Radiometry and photometry,” in Modern Optical Engineering (Academic, 2000), pp. 19–249.

M. Born and E. Wolf, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light (Academic, 2005).

FLIR, The Ultimate Infrared Handbook for R&D Professionals (Academic, 2009).

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Figures (12)

Fig. 1.
Fig. 1.

(a) Backward ray tracing. (b) Forward ray tracing.

Fig. 2.
Fig. 2.

Geometry of stray lights. (a) Path of the stray light bundle. (b) Emitting of the light bundle. (c) Absorbing of the light bundle.

Fig. 3.
Fig. 3.

Tracing and calculating process of stray lights.

Fig. 4.
Fig. 4.

(a) Structure of the example system. (b) Warm shield.

Fig. 5.
Fig. 5.

MTF curves of the lens.

Fig. 6.
Fig. 6.

Typical images of the example system.

Fig. 7.
Fig. 7.

Zero-order stray radiation irradiance one-dimensional (1D).

Fig. 8.
Fig. 8.

First-order stray radiation irradiance (1D).

Fig. 9.
Fig. 9.

Total stray radiation irradiance (1D).

Fig. 10.
Fig. 10.

Total stray radiation irradiance (2D).

Fig. 11.
Fig. 11.

(a) Optics of the example system. (b) Model for ray tracing.

Fig. 12.
Fig. 12.

Narcissus irradiance on the detector diagonal line. (a) Result of forward ray tracing. (b) Result of the improved backward ray tracing.

Tables (3)

Tables Icon

Table 1. Primary Parameters of the Optics

Tables Icon

Table 2. Surface Properties Assigned to the Relevant Elements

Tables Icon

Table 3. Primary Parameters of the Optics

Equations (9)

Equations on this page are rendered with MathJax. Learn more.

N=N(λ,T)ε(θ,φ,λ,T)Pn2/n2,
d2B=NdScos4θh2αλdλ,
d2B=N(λ,T)ε(θ,φ,λ,T)Pn2n2dScos4θh2αλdλ.
P=α(θ,φ,λ,T)d2Ed2E,
d2B=N(λ,T)ε(θ,φ,λ,T)α(θ,φ,λ,T)n2n2d2Ed2E/((dScos4θ/h2)dλ)αλ.
d2B=N(λ,T)ε(θ,φ,λ,T)α(θ,φ,λ,T)n2n2αλd2E.
B=λAN(λ,T)ε(θ,φ,λ,T)α(θ,φ,λ,T)n2n2αλd2E.
B=λAn2n2N(λ,T)αλd2E.
B=i=1Qk=1Mni2ni,k2N(λi,Tk)αλΔEi,k,

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