Abstract

Spot distortion caused by astigmatism effect in orthogonal cylindrical lenses is utilized to measure axial displacement with 30 nm resolution, strong noise immunity, and compact experiment setup. Axial displacement of the sample surface is determined by four-quadrant difference processing of distorted laser spots’ energy distribution images received by CCD. Four-quadrant difference processing results indicate an applicable measuring range of 5.6 μm (cubic fitting r=0.9988) with a highly linear range of 1.2 μm (linear fitting r=0.9996). Factors affecting measuring range and sensitivity are analyzed by theoretical deduction and numerical simulation. This technique has potential applications in drifting sample tracking and measurement in advanced microscopy.

© 2012 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. Y. Morimoto, T. Matui, M. Fujigaki, and Y. Yamamoto, “Nano-meter displacement measurement by phase analysis of fringe patterns obtained by optical methods,” Exp. Mech. 21, 20–34 (2006).
  2. X. Li, “Displacement measurement based on the Moire fringe,” Proc. SPIE 8321, 832148 (2011).
    [CrossRef]
  3. S. L. Yeh, S. T. Lin, and Y. H. Chang, “Precise displacement measurement for a local surface,” Opt. Lett. 34, 3406–3408 (2009).
    [CrossRef]
  4. I. Hwang, E. Hwu, and K. Hwang, U. S. patent 7,804,605 B2 (28Sept.2010).
  5. K. S. Yen and M. M. Ratnam, “Comparison of in-plane displacement measurement from circular grating moiré fringes using Fourier transformation and graphical analysis,” Opt. Lasers Eng. 50, 687–702 (2012).
    [CrossRef]
  6. K. Yen and M. Ratnam, “In-plane displacement sensing from circular grating moire fringes using graphical analysis approach,” Sens. Rev. 31, 358–367 (2011).
    [CrossRef]
  7. P. M. B. S. Girao, O. A. Postolache, J. A. B. Faria, and J. M. C. D. Pereira, “An overview and a contribution to the optical measurement of linear displacement,” IEEE Sens. J. 1, 322–331 (2001).
    [CrossRef]
  8. K. Madanipour and M. T. Tavassoly, “Submicron displacements measurement by measuring autocorrelation of the transmission function of a grating,” Proc. SPIE 8082, 808230-7 (2011).
  9. N. Bobroff, “Recent advances in displacement measuring interferometry,” Meas. Sci. Technol. 4, 907–926 (1993).
    [CrossRef]
  10. W.-S. Sun, K.-D. Liu, J.-W. Pan, C.-L. Tien, and M.-S. Hsieh, “Laser expander design of highly efficient Blu-ray disc pickup head,” Opt. Express 17, 2235–2246 (2009).
    [CrossRef]
  11. H. Liu, X. Huang, L. Liu, and Y. Hu, “Designing a coupler for the intersatellite optical communication system,” Optik 119, 608–611 (2008).
  12. C.-H. Liu and Z.-H. Li, “Application of the astigmatic method to the thickness measurement of glass substrates,” Appl. Opt. 47, 3968–3972 (2008).
    [CrossRef]
  13. H. W. Guo, R. Q. Liu, Z. Q. Deng, and Q. S. Wu, “Performance analysis and testing of four-quadrant position sensitive detector,” Adv. Mater. Res. 317–319, 1107–1113 (2011).
    [CrossRef]
  14. K. Bertilsson, E. Dubaric, G. Thungström, H. E. Nilsson, and C. S. Petersson, “Simulation of a low atmospheric-noise modified four-quadrant position sensitive detector,” Nucl. Instrum. Methods Phys. Res. A 466, 183–187 (2001).
    [CrossRef]
  15. A. J. Makynen, J. T. Kostamovaara, and R. A. Myllyla, “A high-resolution lateral displacement sensing method using active illumination of a cooperative target and a focused four-quadrant position-sensitive detector,” IEEE Trans. Instrum. Meas. 44, 46–52 (1995).
    [CrossRef]
  16. L. Pang, U. Levy, K. Campbell, A. Groisman, and Y. Fainman, “Set of two orthogonal adaptive cylindrical lenses in a monolith elastomer device,” Opt. Express 13, 9003–9013(2005).
    [CrossRef]
  17. L. S. Pedrotti and F. L. Pedrotti, Optics and Vision (Prentice Hall, 1998).
  18. J. A. Arnaud and H. Kogelnik, “Gaussian light beams with general astigmatism,” Appl. Opt. 8, 1687–1693 (1969).
    [CrossRef]
  19. A. E. Attard, “Matrix optical analysis of skew rays in mixed systems of spherical and orthogonal cylindrical lenses,” Appl. Opt. 23, 2706–2709 (1984).
    [CrossRef]
  20. L. Te-Tan, “A skew ray tracing-based approach to the error analysis of optical elements with flat boundary surfaces,” Optik 119, 713–722 (2008).
    [CrossRef]
  21. K. Chen, H. Yang, L. Sun, and G. Jin, “Generalized method for calculating astigmatism of the unit-magnification multipass system,” Appl. Opt. 49, 1964–1971 (2010).
    [CrossRef]
  22. G. Nemes and A. E. Siegman, “Measurement of all ten second-order moments of an astigmatic beam by the use of rotating simple astigmatic (anamorphic) optics,” J. Opt. Soc. Am. A 11, 2257–2264 (1994).
    [CrossRef]
  23. ASAP Reference Manual Version 7.5.0 (Breault Research Organization, 2003).
  24. M. Mansuripur, “Distribution of light at and near the focus of high-numerical-aperture objectives,” J. Opt. Soc. Am. A 3, 2086–2093 (1986).
    [CrossRef]
  25. M. R. Beversluis, G. W. Bryant, and S. J. Stranick, “Effects of inhomogeneous fields in superresolving structured-illumination microscopy,” J. Opt. Soc. Am. A 25, 1371–1377 (2008).
    [CrossRef]

2012 (1)

K. S. Yen and M. M. Ratnam, “Comparison of in-plane displacement measurement from circular grating moiré fringes using Fourier transformation and graphical analysis,” Opt. Lasers Eng. 50, 687–702 (2012).
[CrossRef]

2011 (4)

K. Yen and M. Ratnam, “In-plane displacement sensing from circular grating moire fringes using graphical analysis approach,” Sens. Rev. 31, 358–367 (2011).
[CrossRef]

X. Li, “Displacement measurement based on the Moire fringe,” Proc. SPIE 8321, 832148 (2011).
[CrossRef]

K. Madanipour and M. T. Tavassoly, “Submicron displacements measurement by measuring autocorrelation of the transmission function of a grating,” Proc. SPIE 8082, 808230-7 (2011).

H. W. Guo, R. Q. Liu, Z. Q. Deng, and Q. S. Wu, “Performance analysis and testing of four-quadrant position sensitive detector,” Adv. Mater. Res. 317–319, 1107–1113 (2011).
[CrossRef]

2010 (1)

2009 (2)

2008 (4)

H. Liu, X. Huang, L. Liu, and Y. Hu, “Designing a coupler for the intersatellite optical communication system,” Optik 119, 608–611 (2008).

C.-H. Liu and Z.-H. Li, “Application of the astigmatic method to the thickness measurement of glass substrates,” Appl. Opt. 47, 3968–3972 (2008).
[CrossRef]

L. Te-Tan, “A skew ray tracing-based approach to the error analysis of optical elements with flat boundary surfaces,” Optik 119, 713–722 (2008).
[CrossRef]

M. R. Beversluis, G. W. Bryant, and S. J. Stranick, “Effects of inhomogeneous fields in superresolving structured-illumination microscopy,” J. Opt. Soc. Am. A 25, 1371–1377 (2008).
[CrossRef]

2006 (1)

Y. Morimoto, T. Matui, M. Fujigaki, and Y. Yamamoto, “Nano-meter displacement measurement by phase analysis of fringe patterns obtained by optical methods,” Exp. Mech. 21, 20–34 (2006).

2005 (1)

2001 (2)

K. Bertilsson, E. Dubaric, G. Thungström, H. E. Nilsson, and C. S. Petersson, “Simulation of a low atmospheric-noise modified four-quadrant position sensitive detector,” Nucl. Instrum. Methods Phys. Res. A 466, 183–187 (2001).
[CrossRef]

P. M. B. S. Girao, O. A. Postolache, J. A. B. Faria, and J. M. C. D. Pereira, “An overview and a contribution to the optical measurement of linear displacement,” IEEE Sens. J. 1, 322–331 (2001).
[CrossRef]

1995 (1)

A. J. Makynen, J. T. Kostamovaara, and R. A. Myllyla, “A high-resolution lateral displacement sensing method using active illumination of a cooperative target and a focused four-quadrant position-sensitive detector,” IEEE Trans. Instrum. Meas. 44, 46–52 (1995).
[CrossRef]

1994 (1)

1993 (1)

N. Bobroff, “Recent advances in displacement measuring interferometry,” Meas. Sci. Technol. 4, 907–926 (1993).
[CrossRef]

1986 (1)

1984 (1)

1969 (1)

Arnaud, J. A.

Attard, A. E.

Bertilsson, K.

K. Bertilsson, E. Dubaric, G. Thungström, H. E. Nilsson, and C. S. Petersson, “Simulation of a low atmospheric-noise modified four-quadrant position sensitive detector,” Nucl. Instrum. Methods Phys. Res. A 466, 183–187 (2001).
[CrossRef]

Beversluis, M. R.

Bobroff, N.

N. Bobroff, “Recent advances in displacement measuring interferometry,” Meas. Sci. Technol. 4, 907–926 (1993).
[CrossRef]

Bryant, G. W.

Campbell, K.

Chang, Y. H.

Chen, K.

Deng, Z. Q.

H. W. Guo, R. Q. Liu, Z. Q. Deng, and Q. S. Wu, “Performance analysis and testing of four-quadrant position sensitive detector,” Adv. Mater. Res. 317–319, 1107–1113 (2011).
[CrossRef]

Dubaric, E.

K. Bertilsson, E. Dubaric, G. Thungström, H. E. Nilsson, and C. S. Petersson, “Simulation of a low atmospheric-noise modified four-quadrant position sensitive detector,” Nucl. Instrum. Methods Phys. Res. A 466, 183–187 (2001).
[CrossRef]

Fainman, Y.

Faria, J. A. B.

P. M. B. S. Girao, O. A. Postolache, J. A. B. Faria, and J. M. C. D. Pereira, “An overview and a contribution to the optical measurement of linear displacement,” IEEE Sens. J. 1, 322–331 (2001).
[CrossRef]

Fujigaki, M.

Y. Morimoto, T. Matui, M. Fujigaki, and Y. Yamamoto, “Nano-meter displacement measurement by phase analysis of fringe patterns obtained by optical methods,” Exp. Mech. 21, 20–34 (2006).

Girao, P. M. B. S.

P. M. B. S. Girao, O. A. Postolache, J. A. B. Faria, and J. M. C. D. Pereira, “An overview and a contribution to the optical measurement of linear displacement,” IEEE Sens. J. 1, 322–331 (2001).
[CrossRef]

Groisman, A.

Guo, H. W.

H. W. Guo, R. Q. Liu, Z. Q. Deng, and Q. S. Wu, “Performance analysis and testing of four-quadrant position sensitive detector,” Adv. Mater. Res. 317–319, 1107–1113 (2011).
[CrossRef]

Hsieh, M.-S.

Hu, Y.

H. Liu, X. Huang, L. Liu, and Y. Hu, “Designing a coupler for the intersatellite optical communication system,” Optik 119, 608–611 (2008).

Huang, X.

H. Liu, X. Huang, L. Liu, and Y. Hu, “Designing a coupler for the intersatellite optical communication system,” Optik 119, 608–611 (2008).

Hwang, I.

I. Hwang, E. Hwu, and K. Hwang, U. S. patent 7,804,605 B2 (28Sept.2010).

Hwang, K.

I. Hwang, E. Hwu, and K. Hwang, U. S. patent 7,804,605 B2 (28Sept.2010).

Hwu, E.

I. Hwang, E. Hwu, and K. Hwang, U. S. patent 7,804,605 B2 (28Sept.2010).

Jin, G.

Kogelnik, H.

Kostamovaara, J. T.

A. J. Makynen, J. T. Kostamovaara, and R. A. Myllyla, “A high-resolution lateral displacement sensing method using active illumination of a cooperative target and a focused four-quadrant position-sensitive detector,” IEEE Trans. Instrum. Meas. 44, 46–52 (1995).
[CrossRef]

Levy, U.

Li, X.

X. Li, “Displacement measurement based on the Moire fringe,” Proc. SPIE 8321, 832148 (2011).
[CrossRef]

Li, Z.-H.

Lin, S. T.

Liu, C.-H.

Liu, H.

H. Liu, X. Huang, L. Liu, and Y. Hu, “Designing a coupler for the intersatellite optical communication system,” Optik 119, 608–611 (2008).

Liu, K.-D.

Liu, L.

H. Liu, X. Huang, L. Liu, and Y. Hu, “Designing a coupler for the intersatellite optical communication system,” Optik 119, 608–611 (2008).

Liu, R. Q.

H. W. Guo, R. Q. Liu, Z. Q. Deng, and Q. S. Wu, “Performance analysis and testing of four-quadrant position sensitive detector,” Adv. Mater. Res. 317–319, 1107–1113 (2011).
[CrossRef]

Madanipour, K.

K. Madanipour and M. T. Tavassoly, “Submicron displacements measurement by measuring autocorrelation of the transmission function of a grating,” Proc. SPIE 8082, 808230-7 (2011).

Makynen, A. J.

A. J. Makynen, J. T. Kostamovaara, and R. A. Myllyla, “A high-resolution lateral displacement sensing method using active illumination of a cooperative target and a focused four-quadrant position-sensitive detector,” IEEE Trans. Instrum. Meas. 44, 46–52 (1995).
[CrossRef]

Mansuripur, M.

Matui, T.

Y. Morimoto, T. Matui, M. Fujigaki, and Y. Yamamoto, “Nano-meter displacement measurement by phase analysis of fringe patterns obtained by optical methods,” Exp. Mech. 21, 20–34 (2006).

Morimoto, Y.

Y. Morimoto, T. Matui, M. Fujigaki, and Y. Yamamoto, “Nano-meter displacement measurement by phase analysis of fringe patterns obtained by optical methods,” Exp. Mech. 21, 20–34 (2006).

Myllyla, R. A.

A. J. Makynen, J. T. Kostamovaara, and R. A. Myllyla, “A high-resolution lateral displacement sensing method using active illumination of a cooperative target and a focused four-quadrant position-sensitive detector,” IEEE Trans. Instrum. Meas. 44, 46–52 (1995).
[CrossRef]

Nemes, G.

Nilsson, H. E.

K. Bertilsson, E. Dubaric, G. Thungström, H. E. Nilsson, and C. S. Petersson, “Simulation of a low atmospheric-noise modified four-quadrant position sensitive detector,” Nucl. Instrum. Methods Phys. Res. A 466, 183–187 (2001).
[CrossRef]

Pan, J.-W.

Pang, L.

Pedrotti, F. L.

L. S. Pedrotti and F. L. Pedrotti, Optics and Vision (Prentice Hall, 1998).

Pedrotti, L. S.

L. S. Pedrotti and F. L. Pedrotti, Optics and Vision (Prentice Hall, 1998).

Pereira, J. M. C. D.

P. M. B. S. Girao, O. A. Postolache, J. A. B. Faria, and J. M. C. D. Pereira, “An overview and a contribution to the optical measurement of linear displacement,” IEEE Sens. J. 1, 322–331 (2001).
[CrossRef]

Petersson, C. S.

K. Bertilsson, E. Dubaric, G. Thungström, H. E. Nilsson, and C. S. Petersson, “Simulation of a low atmospheric-noise modified four-quadrant position sensitive detector,” Nucl. Instrum. Methods Phys. Res. A 466, 183–187 (2001).
[CrossRef]

Postolache, O. A.

P. M. B. S. Girao, O. A. Postolache, J. A. B. Faria, and J. M. C. D. Pereira, “An overview and a contribution to the optical measurement of linear displacement,” IEEE Sens. J. 1, 322–331 (2001).
[CrossRef]

Ratnam, M.

K. Yen and M. Ratnam, “In-plane displacement sensing from circular grating moire fringes using graphical analysis approach,” Sens. Rev. 31, 358–367 (2011).
[CrossRef]

Ratnam, M. M.

K. S. Yen and M. M. Ratnam, “Comparison of in-plane displacement measurement from circular grating moiré fringes using Fourier transformation and graphical analysis,” Opt. Lasers Eng. 50, 687–702 (2012).
[CrossRef]

Siegman, A. E.

Stranick, S. J.

Sun, L.

Sun, W.-S.

Tavassoly, M. T.

K. Madanipour and M. T. Tavassoly, “Submicron displacements measurement by measuring autocorrelation of the transmission function of a grating,” Proc. SPIE 8082, 808230-7 (2011).

Te-Tan, L.

L. Te-Tan, “A skew ray tracing-based approach to the error analysis of optical elements with flat boundary surfaces,” Optik 119, 713–722 (2008).
[CrossRef]

Thungström, G.

K. Bertilsson, E. Dubaric, G. Thungström, H. E. Nilsson, and C. S. Petersson, “Simulation of a low atmospheric-noise modified four-quadrant position sensitive detector,” Nucl. Instrum. Methods Phys. Res. A 466, 183–187 (2001).
[CrossRef]

Tien, C.-L.

Wu, Q. S.

H. W. Guo, R. Q. Liu, Z. Q. Deng, and Q. S. Wu, “Performance analysis and testing of four-quadrant position sensitive detector,” Adv. Mater. Res. 317–319, 1107–1113 (2011).
[CrossRef]

Yamamoto, Y.

Y. Morimoto, T. Matui, M. Fujigaki, and Y. Yamamoto, “Nano-meter displacement measurement by phase analysis of fringe patterns obtained by optical methods,” Exp. Mech. 21, 20–34 (2006).

Yang, H.

Yeh, S. L.

Yen, K.

K. Yen and M. Ratnam, “In-plane displacement sensing from circular grating moire fringes using graphical analysis approach,” Sens. Rev. 31, 358–367 (2011).
[CrossRef]

Yen, K. S.

K. S. Yen and M. M. Ratnam, “Comparison of in-plane displacement measurement from circular grating moiré fringes using Fourier transformation and graphical analysis,” Opt. Lasers Eng. 50, 687–702 (2012).
[CrossRef]

Adv. Mater. Res. (1)

H. W. Guo, R. Q. Liu, Z. Q. Deng, and Q. S. Wu, “Performance analysis and testing of four-quadrant position sensitive detector,” Adv. Mater. Res. 317–319, 1107–1113 (2011).
[CrossRef]

Appl. Opt. (4)

Exp. Mech. (1)

Y. Morimoto, T. Matui, M. Fujigaki, and Y. Yamamoto, “Nano-meter displacement measurement by phase analysis of fringe patterns obtained by optical methods,” Exp. Mech. 21, 20–34 (2006).

IEEE Sens. J. (1)

P. M. B. S. Girao, O. A. Postolache, J. A. B. Faria, and J. M. C. D. Pereira, “An overview and a contribution to the optical measurement of linear displacement,” IEEE Sens. J. 1, 322–331 (2001).
[CrossRef]

IEEE Trans. Instrum. Meas. (1)

A. J. Makynen, J. T. Kostamovaara, and R. A. Myllyla, “A high-resolution lateral displacement sensing method using active illumination of a cooperative target and a focused four-quadrant position-sensitive detector,” IEEE Trans. Instrum. Meas. 44, 46–52 (1995).
[CrossRef]

J. Opt. Soc. Am. A (3)

Meas. Sci. Technol. (1)

N. Bobroff, “Recent advances in displacement measuring interferometry,” Meas. Sci. Technol. 4, 907–926 (1993).
[CrossRef]

Nucl. Instrum. Methods Phys. Res. A (1)

K. Bertilsson, E. Dubaric, G. Thungström, H. E. Nilsson, and C. S. Petersson, “Simulation of a low atmospheric-noise modified four-quadrant position sensitive detector,” Nucl. Instrum. Methods Phys. Res. A 466, 183–187 (2001).
[CrossRef]

Opt. Express (2)

Opt. Lasers Eng. (1)

K. S. Yen and M. M. Ratnam, “Comparison of in-plane displacement measurement from circular grating moiré fringes using Fourier transformation and graphical analysis,” Opt. Lasers Eng. 50, 687–702 (2012).
[CrossRef]

Opt. Lett. (1)

Optik (2)

L. Te-Tan, “A skew ray tracing-based approach to the error analysis of optical elements with flat boundary surfaces,” Optik 119, 713–722 (2008).
[CrossRef]

H. Liu, X. Huang, L. Liu, and Y. Hu, “Designing a coupler for the intersatellite optical communication system,” Optik 119, 608–611 (2008).

Proc. SPIE (2)

X. Li, “Displacement measurement based on the Moire fringe,” Proc. SPIE 8321, 832148 (2011).
[CrossRef]

K. Madanipour and M. T. Tavassoly, “Submicron displacements measurement by measuring autocorrelation of the transmission function of a grating,” Proc. SPIE 8082, 808230-7 (2011).

Sens. Rev. (1)

K. Yen and M. Ratnam, “In-plane displacement sensing from circular grating moire fringes using graphical analysis approach,” Sens. Rev. 31, 358–367 (2011).
[CrossRef]

Other (3)

I. Hwang, E. Hwu, and K. Hwang, U. S. patent 7,804,605 B2 (28Sept.2010).

L. S. Pedrotti and F. L. Pedrotti, Optics and Vision (Prentice Hall, 1998).

ASAP Reference Manual Version 7.5.0 (Breault Research Organization, 2003).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (12)

Fig. 1.
Fig. 1.

Crossed cylindrical lenses (L1 and L2 are orthogonal cylindrical lenses).

Fig. 2.
Fig. 2.

Simulation of different beam cross sections based on Eq. (5); f=150mm, d1=20mm, d2 equals (a) 130 mm; (b) 135 mm; (c) 140 mm; (d) 145 mm; (e) 150 mm.

Fig. 3.
Fig. 3.

Simulated relationship between Δ and(d2,f), where f=150mm and d1=20mm. Pseudocolor indicates the value of Δ in millimeters. White line consists of void values.

Fig. 4.
Fig. 4.

Schematic of simulated experiment setup. L1 and L2 are orthogonal cylindrical lenses. L3 is the focusing lens with short focal length.

Fig. 5.
Fig. 5.

ASAP solid model of experiment setup. Components: 1, Gaussian laser source (Zlocation=40mm, Zwaist_location=0mm, beam width=0.9mm); 2, beam splitter; 3, plano-convex cylindrical lens 1 (f=150mm, ϕ=20mm, angle α between lens’ focal line and horizontal plane is 90°); 4, plano-convex cylindrical lens 2 (f=150mm, ϕ=20mm, α=0°); 5, focusing lens (f=2mm, ϕ=5.4mm, thickness=1mm); 6, plane mirror; 7, image focusing lens (f=300mm, ϕ=20mm); 8, detector plane. Element spacing parameters: axial distance between two cylindrical lenses d1=20mm; axial distance between cylindrical lens 2 and focusing lens d2=90mm; axial distance between focusing lens and plane mirrord3=2.808mm; axial distance between image focusing lens and detector plane d4=300mm.

Fig. 6.
Fig. 6.

ASAP-simulated distorted laser spot when Δd3 equals (a) 1μm, (b) 0 μm, (c) 1 μm, (d) 2 μm, (e) 3 μm, (f) 4 μm, (g) 5 μm, (h) 6 μm.

Fig. 7.
Fig. 7.

(a). N.A. vs. d2 (b). Equivalent focal depth vs. N.A.

Fig. 8.
Fig. 8.

(a) Schematic configuration of astigmatism displacement measuring system. (b) Real system: 1, light source; 2, 5×objective lens (NA=0.15); 3, beam splitter; 4, plano-convex cylindrical lens 1 (f=150mm, ϕ=20mm, angle α between lens’ focal line and horizontal plane is 45°); 5, plano-convex cylindrical lens 2 (f=150mm, ϕ=20mm, α=135°); 6, 100× objective lens (f=2mm, NA=0.8); 7, sample; 8, nanopositioner (Thorlabs NanoMax-TS); 9, singlet lens (f=300mm); 10, light attenuator; 11, Beam-On HR CCD laser beam profiler.

Fig. 9.
Fig. 9.

Distorted laser spots (false color) corresponding to samples with relative displacements of (a) 0 μm; (b) 0.8 μm; (c) 1.6 μm; (d) 2.4 μm; (e) 3.2 μm; (f) 4.0 μm; (g) 4.8 μm; (h) 5.6 μm.

Fig. 10.
Fig. 10.

Layout of data processing models: (a) HFWHM model, (b) FQD model.

Fig. 11.
Fig. 11.

HFWHM processing model.

Fig. 12.
Fig. 12.

FQD processing model.

Equations (8)

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

Ri=[xiyiuivi],Ri=[xiyiuivi],Ri=LiRi,Ri=Ti1di1Ri1,
Liαi=(10000100sin2αifisinαcosαfi10sinαcosαficos2αifi01).
Tidi=[10di0010di00100001].
Rimage=T2d2L2π2T1d1L10Rsource.
[ximageyimageuimagevimage]=[10d20010d200100001][100001001f20100001][10d10010d100100001][10000100001001f101][x0y000]=[x0(1d2f2)y0(1d1+d2f1)x0f2y0f1].
Rimage=T3d3LfocusT2d2L2π2T1d1L10Rsource=[ximageyimageuimagevimage]=[x0(1d2(fd3)+d3(f+f)ff)y0(1(d1+d2)(fd3)+d3(f+f)ff)x0(d2ffff)y0(d1+d2ffff)].
Δ(d2,f)=d3|ximage=0d3|yimage=0=d1f2(f+fd2)(f+fd1d2).
FES=i=A,Cenergy ofith quadranti=B,Denergy ofith quadranti=A,B,C,Denergy ofith quadrant.

Metrics