Abstract

One approach to aberration compensation of an imaging system is to introduce a suitable phase mask at the aperture plane of an imaging system. We utilize this principle for the compensation of astigmatism. A suitable polarization mask used on the aperture plane together with a polarizer-retarder combination at the input of the imaging system provides the compensating polarization-induced phase steps at different quadrants of the apertures masked by different polarizers. The aberrant phase can be considerably compensated by the proper choice of a polarization mask and suitable selection of the polarization parameters involved. The results presented here bear out our theoretical expectation.

© 2004 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. N. Lopez-Gil, H. C. Howland, B. Howland, N. Charman, R. Applegate, “Generation of third-order spherical aberration and coma aberrations by use of radially symmetric fourth-order lenses,” J. Opt. Soc. Am. A 15, 2563–2571 (1998).
    [CrossRef]
  2. N. Chateau, A. Blanchard, D. Baude, “Influence of myopia and aging on the optimal spherical aberration of soft contact lenses,” J. Opt. Soc. Am. A 15, 2589–2596 (1998).
    [CrossRef]
  3. J. E. Harvey, G. M. Callahan, M. Gray, “Wavefront error compensation capabilities of multi-actuator deformable mirrors,” in Adaptive Optical Components I, S. Holly, ed., SPIE Proc.141, 50–57( 1978).
    [CrossRef]
  4. J. Feinleib, S. G. Lipson, P. F. Cone, “Monolithic piezoelectric mirror for wavefront correction,” Appl. Phys. Lett. 25, 311–313 (1974).
    [CrossRef]
  5. L. Zhu, P.-C. Sun, D.-U. Bartsch, W. R. Freeman, Y. Fainmann, “Adaptive control of a membrane deformable mirror for aberration compensation,” Appl. Opt. 38, 168–176 (1999).
    [CrossRef]
  6. G. D. Love, “Wavefront correction and production of Zernike modes with a liquid crystal spatial light modulator,” Appl. Opt. 36, 1517–1524 (1997).
    [CrossRef] [PubMed]
  7. B. Schmidt, “Ein lichtstarkes komafreies Spiegelsystem (a bright coma-free mirror system),” Zeitung. Opt. Mech. 52, 79 (1931).
  8. A. K. Chakraborty, H. Mukherjee, “Modification of PSF by polarization mask,” J. Opt. (India) 5, 71–74 (1976).
  9. A. K. Chakraborty, B. Mondol Adhikari, P. Roychoudhury, “The optical transfer function of a perfect lens with polarization mask,” J. Opt. (Paris) 9, 251–254 (1978).
    [CrossRef]
  10. A. Ghosh, A. K. Chakraborty, K. Murata, “Imaging characteristics of a perfect lens partially masked by a linear polarizer,” Optik Stuttgart 76, 153–156 (1987).
  11. A. Ghosh, J. Basu, P. P. Goswami, A. K. Chakraborty, “Frequency response characteristics of a perfect lens partially masked by a retarder,” J. Mod. Opt. 34, 281–289 (1987).
    [CrossRef]
  12. A. Ghosh, K. Murata, A. K. Chakraborty, “Frequency response characteristics of a perfect lens masked by polarizing devices,” J. Opt. Soc. Am. A 5, 277–284 (1988).
    [CrossRef]
  13. K. Bhattacharya, A. Ghosh, A. K. Chakraborty, “Realization of phase and amplitude steps on lens aperture using polarization masks,” J. Opt. (India) 20, 128–131 (1991).
  14. K. Bhattacharya, A. Ghosh, A. K. Chakraborty, “Vector wave imagery with a lens masked by polarizers,” J. Mod. Opt. 40, 379–390 (1993).
    [CrossRef]
  15. K. Bhattacharya, A. K. Chakraborty, A. Ghosh, “Simulation of effects of phase and amplitude coatings on the lens aperture with polarization masks,” J. Opt. Soc. Am. A 2, 586–592 (1994).
    [CrossRef]
  16. S. N. Datta, A. Ghosh, A. K. Chakraborty, “Imaging characteristics of a lens zonally masked by polarizers and retarder,” Optik Stuttgart 100, 1–7 (1995).
  17. D. R. Chowdhury, K. Bhattacharya, A. K. Chakroborty, “Possibility of optical focal shift with polarization masks,” Appl. Opt. 42, 3819–3826 (2003).
    [CrossRef] [PubMed]
  18. D. R. Chowdhury, K. Bhattacharya, S. Sanyal, A. K. Chakraborty, “Performance of a polarization-masked lens aperture in the presence of spherical aberration,” J. Opt. A 4, 98–104 (2002).
    [CrossRef]
  19. R. Barakat, A. Houston, “Transfer function of an optical system in the presence of off-axis aberrations,” J. Opt. Soc. Am. 55, 1142–1148 (1965).
    [CrossRef]
  20. R. Barakat, A. Houston, “Line spread function and edge spread function in the presence of off-axis aberrations,” J. Opt. Soc. Am. 55, 1132–1135 (1965).
    [CrossRef]
  21. V. N. Mahajan, Aberration Theory Made Simple (SPIE Optical Engineering Press, Bellingham, Wash., 1991).
    [CrossRef]
  22. Y. Fainman, J. Shamir, “Polarization of nonplanar wavefronts,” Appl. Opt. 23, 3188–3194 (1984).
    [CrossRef] [PubMed]
  23. R. A. Chipman, “Polarization analysis of optical systems,” Opt. Eng. 28, 90–99 (1989).
  24. J. McGuire, R. Chipman, “Polarization aberrations I: Rotationally symmetric optical systems,” Appl. Opt. 33, 5080–5100 (1994).
    [CrossRef] [PubMed]
  25. J. McGuire, R. Chipman, “Polarization aberrations II: tilted and decentered optical systems,” Appl. Opt. 33, 5101–5107 (1994).
    [CrossRef] [PubMed]
  26. J. McGuire, R. Chipman, “Diffraction image formation in optical systems with polarization aberrations II: Amplitude response matrices for rotationally symmetric systems,” J. Opt. Soc. Am. A 7, 1614–1626 (1990).
    [CrossRef]
  27. N. Mukunda, R. Simon, E. C. G. Sudarshan, “Fourier optics for the Maxwell field: formalism and applications,” J. Opt. Soc. Am. A 2, 416–420 (1985).
    [CrossRef]
  28. J. Linares, “Maxwell paraxial wave optics in inhomogeneous media by path integral formalism,” Phys. Lett. A 141, 207–212 (1989).
    [CrossRef]
  29. A. I. Mahan, C. V. Bitterli, S. M. Cannon, “Far field diffraction patterns of single and multiple apertures bounded by arcs and radii of concentric circles,” J. Opt. Soc. Am. 54, 721–744 (1964).
    [CrossRef]
  30. H. H. Hopkins, Wave Theory of Aberrations (Clarendon, Oxford, 1950).

2003

2002

D. R. Chowdhury, K. Bhattacharya, S. Sanyal, A. K. Chakraborty, “Performance of a polarization-masked lens aperture in the presence of spherical aberration,” J. Opt. A 4, 98–104 (2002).
[CrossRef]

1999

1998

1997

1995

S. N. Datta, A. Ghosh, A. K. Chakraborty, “Imaging characteristics of a lens zonally masked by polarizers and retarder,” Optik Stuttgart 100, 1–7 (1995).

1994

1993

K. Bhattacharya, A. Ghosh, A. K. Chakraborty, “Vector wave imagery with a lens masked by polarizers,” J. Mod. Opt. 40, 379–390 (1993).
[CrossRef]

1991

K. Bhattacharya, A. Ghosh, A. K. Chakraborty, “Realization of phase and amplitude steps on lens aperture using polarization masks,” J. Opt. (India) 20, 128–131 (1991).

1990

1989

J. Linares, “Maxwell paraxial wave optics in inhomogeneous media by path integral formalism,” Phys. Lett. A 141, 207–212 (1989).
[CrossRef]

R. A. Chipman, “Polarization analysis of optical systems,” Opt. Eng. 28, 90–99 (1989).

1988

1987

A. Ghosh, A. K. Chakraborty, K. Murata, “Imaging characteristics of a perfect lens partially masked by a linear polarizer,” Optik Stuttgart 76, 153–156 (1987).

A. Ghosh, J. Basu, P. P. Goswami, A. K. Chakraborty, “Frequency response characteristics of a perfect lens partially masked by a retarder,” J. Mod. Opt. 34, 281–289 (1987).
[CrossRef]

1985

1984

1978

A. K. Chakraborty, B. Mondol Adhikari, P. Roychoudhury, “The optical transfer function of a perfect lens with polarization mask,” J. Opt. (Paris) 9, 251–254 (1978).
[CrossRef]

1976

A. K. Chakraborty, H. Mukherjee, “Modification of PSF by polarization mask,” J. Opt. (India) 5, 71–74 (1976).

1974

J. Feinleib, S. G. Lipson, P. F. Cone, “Monolithic piezoelectric mirror for wavefront correction,” Appl. Phys. Lett. 25, 311–313 (1974).
[CrossRef]

1965

1964

1931

B. Schmidt, “Ein lichtstarkes komafreies Spiegelsystem (a bright coma-free mirror system),” Zeitung. Opt. Mech. 52, 79 (1931).

Applegate, R.

Barakat, R.

Bartsch, D.-U.

Basu, J.

A. Ghosh, J. Basu, P. P. Goswami, A. K. Chakraborty, “Frequency response characteristics of a perfect lens partially masked by a retarder,” J. Mod. Opt. 34, 281–289 (1987).
[CrossRef]

Baude, D.

Bhattacharya, K.

D. R. Chowdhury, K. Bhattacharya, A. K. Chakroborty, “Possibility of optical focal shift with polarization masks,” Appl. Opt. 42, 3819–3826 (2003).
[CrossRef] [PubMed]

D. R. Chowdhury, K. Bhattacharya, S. Sanyal, A. K. Chakraborty, “Performance of a polarization-masked lens aperture in the presence of spherical aberration,” J. Opt. A 4, 98–104 (2002).
[CrossRef]

K. Bhattacharya, A. K. Chakraborty, A. Ghosh, “Simulation of effects of phase and amplitude coatings on the lens aperture with polarization masks,” J. Opt. Soc. Am. A 2, 586–592 (1994).
[CrossRef]

K. Bhattacharya, A. Ghosh, A. K. Chakraborty, “Vector wave imagery with a lens masked by polarizers,” J. Mod. Opt. 40, 379–390 (1993).
[CrossRef]

K. Bhattacharya, A. Ghosh, A. K. Chakraborty, “Realization of phase and amplitude steps on lens aperture using polarization masks,” J. Opt. (India) 20, 128–131 (1991).

Bitterli, C. V.

Blanchard, A.

Callahan, G. M.

J. E. Harvey, G. M. Callahan, M. Gray, “Wavefront error compensation capabilities of multi-actuator deformable mirrors,” in Adaptive Optical Components I, S. Holly, ed., SPIE Proc.141, 50–57( 1978).
[CrossRef]

Cannon, S. M.

Chakraborty, A. K.

D. R. Chowdhury, K. Bhattacharya, S. Sanyal, A. K. Chakraborty, “Performance of a polarization-masked lens aperture in the presence of spherical aberration,” J. Opt. A 4, 98–104 (2002).
[CrossRef]

S. N. Datta, A. Ghosh, A. K. Chakraborty, “Imaging characteristics of a lens zonally masked by polarizers and retarder,” Optik Stuttgart 100, 1–7 (1995).

K. Bhattacharya, A. K. Chakraborty, A. Ghosh, “Simulation of effects of phase and amplitude coatings on the lens aperture with polarization masks,” J. Opt. Soc. Am. A 2, 586–592 (1994).
[CrossRef]

K. Bhattacharya, A. Ghosh, A. K. Chakraborty, “Vector wave imagery with a lens masked by polarizers,” J. Mod. Opt. 40, 379–390 (1993).
[CrossRef]

K. Bhattacharya, A. Ghosh, A. K. Chakraborty, “Realization of phase and amplitude steps on lens aperture using polarization masks,” J. Opt. (India) 20, 128–131 (1991).

A. Ghosh, K. Murata, A. K. Chakraborty, “Frequency response characteristics of a perfect lens masked by polarizing devices,” J. Opt. Soc. Am. A 5, 277–284 (1988).
[CrossRef]

A. Ghosh, J. Basu, P. P. Goswami, A. K. Chakraborty, “Frequency response characteristics of a perfect lens partially masked by a retarder,” J. Mod. Opt. 34, 281–289 (1987).
[CrossRef]

A. Ghosh, A. K. Chakraborty, K. Murata, “Imaging characteristics of a perfect lens partially masked by a linear polarizer,” Optik Stuttgart 76, 153–156 (1987).

A. K. Chakraborty, B. Mondol Adhikari, P. Roychoudhury, “The optical transfer function of a perfect lens with polarization mask,” J. Opt. (Paris) 9, 251–254 (1978).
[CrossRef]

A. K. Chakraborty, H. Mukherjee, “Modification of PSF by polarization mask,” J. Opt. (India) 5, 71–74 (1976).

Chakroborty, A. K.

Charman, N.

Chateau, N.

Chipman, R.

Chipman, R. A.

R. A. Chipman, “Polarization analysis of optical systems,” Opt. Eng. 28, 90–99 (1989).

Chowdhury, D. R.

D. R. Chowdhury, K. Bhattacharya, A. K. Chakroborty, “Possibility of optical focal shift with polarization masks,” Appl. Opt. 42, 3819–3826 (2003).
[CrossRef] [PubMed]

D. R. Chowdhury, K. Bhattacharya, S. Sanyal, A. K. Chakraborty, “Performance of a polarization-masked lens aperture in the presence of spherical aberration,” J. Opt. A 4, 98–104 (2002).
[CrossRef]

Cone, P. F.

J. Feinleib, S. G. Lipson, P. F. Cone, “Monolithic piezoelectric mirror for wavefront correction,” Appl. Phys. Lett. 25, 311–313 (1974).
[CrossRef]

Datta, S. N.

S. N. Datta, A. Ghosh, A. K. Chakraborty, “Imaging characteristics of a lens zonally masked by polarizers and retarder,” Optik Stuttgart 100, 1–7 (1995).

Fainman, Y.

Fainmann, Y.

Feinleib, J.

J. Feinleib, S. G. Lipson, P. F. Cone, “Monolithic piezoelectric mirror for wavefront correction,” Appl. Phys. Lett. 25, 311–313 (1974).
[CrossRef]

Freeman, W. R.

Ghosh, A.

S. N. Datta, A. Ghosh, A. K. Chakraborty, “Imaging characteristics of a lens zonally masked by polarizers and retarder,” Optik Stuttgart 100, 1–7 (1995).

K. Bhattacharya, A. K. Chakraborty, A. Ghosh, “Simulation of effects of phase and amplitude coatings on the lens aperture with polarization masks,” J. Opt. Soc. Am. A 2, 586–592 (1994).
[CrossRef]

K. Bhattacharya, A. Ghosh, A. K. Chakraborty, “Vector wave imagery with a lens masked by polarizers,” J. Mod. Opt. 40, 379–390 (1993).
[CrossRef]

K. Bhattacharya, A. Ghosh, A. K. Chakraborty, “Realization of phase and amplitude steps on lens aperture using polarization masks,” J. Opt. (India) 20, 128–131 (1991).

A. Ghosh, K. Murata, A. K. Chakraborty, “Frequency response characteristics of a perfect lens masked by polarizing devices,” J. Opt. Soc. Am. A 5, 277–284 (1988).
[CrossRef]

A. Ghosh, A. K. Chakraborty, K. Murata, “Imaging characteristics of a perfect lens partially masked by a linear polarizer,” Optik Stuttgart 76, 153–156 (1987).

A. Ghosh, J. Basu, P. P. Goswami, A. K. Chakraborty, “Frequency response characteristics of a perfect lens partially masked by a retarder,” J. Mod. Opt. 34, 281–289 (1987).
[CrossRef]

Goswami, P. P.

A. Ghosh, J. Basu, P. P. Goswami, A. K. Chakraborty, “Frequency response characteristics of a perfect lens partially masked by a retarder,” J. Mod. Opt. 34, 281–289 (1987).
[CrossRef]

Gray, M.

J. E. Harvey, G. M. Callahan, M. Gray, “Wavefront error compensation capabilities of multi-actuator deformable mirrors,” in Adaptive Optical Components I, S. Holly, ed., SPIE Proc.141, 50–57( 1978).
[CrossRef]

Harvey, J. E.

J. E. Harvey, G. M. Callahan, M. Gray, “Wavefront error compensation capabilities of multi-actuator deformable mirrors,” in Adaptive Optical Components I, S. Holly, ed., SPIE Proc.141, 50–57( 1978).
[CrossRef]

Hopkins, H. H.

H. H. Hopkins, Wave Theory of Aberrations (Clarendon, Oxford, 1950).

Houston, A.

Howland, B.

Howland, H. C.

Linares, J.

J. Linares, “Maxwell paraxial wave optics in inhomogeneous media by path integral formalism,” Phys. Lett. A 141, 207–212 (1989).
[CrossRef]

Lipson, S. G.

J. Feinleib, S. G. Lipson, P. F. Cone, “Monolithic piezoelectric mirror for wavefront correction,” Appl. Phys. Lett. 25, 311–313 (1974).
[CrossRef]

Lopez-Gil, N.

Love, G. D.

Mahajan, V. N.

V. N. Mahajan, Aberration Theory Made Simple (SPIE Optical Engineering Press, Bellingham, Wash., 1991).
[CrossRef]

Mahan, A. I.

McGuire, J.

Mondol Adhikari, B.

A. K. Chakraborty, B. Mondol Adhikari, P. Roychoudhury, “The optical transfer function of a perfect lens with polarization mask,” J. Opt. (Paris) 9, 251–254 (1978).
[CrossRef]

Mukherjee, H.

A. K. Chakraborty, H. Mukherjee, “Modification of PSF by polarization mask,” J. Opt. (India) 5, 71–74 (1976).

Mukunda, N.

Murata, K.

A. Ghosh, K. Murata, A. K. Chakraborty, “Frequency response characteristics of a perfect lens masked by polarizing devices,” J. Opt. Soc. Am. A 5, 277–284 (1988).
[CrossRef]

A. Ghosh, A. K. Chakraborty, K. Murata, “Imaging characteristics of a perfect lens partially masked by a linear polarizer,” Optik Stuttgart 76, 153–156 (1987).

Roychoudhury, P.

A. K. Chakraborty, B. Mondol Adhikari, P. Roychoudhury, “The optical transfer function of a perfect lens with polarization mask,” J. Opt. (Paris) 9, 251–254 (1978).
[CrossRef]

Sanyal, S.

D. R. Chowdhury, K. Bhattacharya, S. Sanyal, A. K. Chakraborty, “Performance of a polarization-masked lens aperture in the presence of spherical aberration,” J. Opt. A 4, 98–104 (2002).
[CrossRef]

Schmidt, B.

B. Schmidt, “Ein lichtstarkes komafreies Spiegelsystem (a bright coma-free mirror system),” Zeitung. Opt. Mech. 52, 79 (1931).

Shamir, J.

Simon, R.

Sudarshan, E. C. G.

Sun, P.-C.

Zhu, L.

Appl. Opt.

Appl. Phys. Lett.

J. Feinleib, S. G. Lipson, P. F. Cone, “Monolithic piezoelectric mirror for wavefront correction,” Appl. Phys. Lett. 25, 311–313 (1974).
[CrossRef]

J. Mod. Opt.

K. Bhattacharya, A. Ghosh, A. K. Chakraborty, “Vector wave imagery with a lens masked by polarizers,” J. Mod. Opt. 40, 379–390 (1993).
[CrossRef]

A. Ghosh, J. Basu, P. P. Goswami, A. K. Chakraborty, “Frequency response characteristics of a perfect lens partially masked by a retarder,” J. Mod. Opt. 34, 281–289 (1987).
[CrossRef]

J. Opt. (India)

A. K. Chakraborty, H. Mukherjee, “Modification of PSF by polarization mask,” J. Opt. (India) 5, 71–74 (1976).

K. Bhattacharya, A. Ghosh, A. K. Chakraborty, “Realization of phase and amplitude steps on lens aperture using polarization masks,” J. Opt. (India) 20, 128–131 (1991).

J. Opt. (Paris)

A. K. Chakraborty, B. Mondol Adhikari, P. Roychoudhury, “The optical transfer function of a perfect lens with polarization mask,” J. Opt. (Paris) 9, 251–254 (1978).
[CrossRef]

J. Opt. A

D. R. Chowdhury, K. Bhattacharya, S. Sanyal, A. K. Chakraborty, “Performance of a polarization-masked lens aperture in the presence of spherical aberration,” J. Opt. A 4, 98–104 (2002).
[CrossRef]

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

Opt. Eng.

R. A. Chipman, “Polarization analysis of optical systems,” Opt. Eng. 28, 90–99 (1989).

Optik Stuttgart

A. Ghosh, A. K. Chakraborty, K. Murata, “Imaging characteristics of a perfect lens partially masked by a linear polarizer,” Optik Stuttgart 76, 153–156 (1987).

S. N. Datta, A. Ghosh, A. K. Chakraborty, “Imaging characteristics of a lens zonally masked by polarizers and retarder,” Optik Stuttgart 100, 1–7 (1995).

Phys. Lett. A

J. Linares, “Maxwell paraxial wave optics in inhomogeneous media by path integral formalism,” Phys. Lett. A 141, 207–212 (1989).
[CrossRef]

Zeitung. Opt. Mech.

B. Schmidt, “Ein lichtstarkes komafreies Spiegelsystem (a bright coma-free mirror system),” Zeitung. Opt. Mech. 52, 79 (1931).

Other

J. E. Harvey, G. M. Callahan, M. Gray, “Wavefront error compensation capabilities of multi-actuator deformable mirrors,” in Adaptive Optical Components I, S. Holly, ed., SPIE Proc.141, 50–57( 1978).
[CrossRef]

V. N. Mahajan, Aberration Theory Made Simple (SPIE Optical Engineering Press, Bellingham, Wash., 1991).
[CrossRef]

H. H. Hopkins, Wave Theory of Aberrations (Clarendon, Oxford, 1950).

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 (11)

Fig. 1
Fig. 1

Schematic diagram of the proposed optical setup: P, polarizer; L, focusing lens; C, compensator; A, analyzer; M, polarization mask; S, screen.

Fig. 2
Fig. 2

Proposed polarization mask.

Fig. 3
Fig. 3

(a) Aperture bounded by radii R 1 and R 2 and azimuths ϕ1 and ϕ2. (b) Sector aperture bounded by radii R 1 = 0 and R 2 = 1 and azimuths ϕ1 and ϕ2.

Fig. 4
Fig. 4

Intensity PSF for a diffraction-limited imaging system.

Fig. 5
Fig. 5

(a) Image of an off-axial point source formed by a clear aperture lens in the presence of astigmatism, w 22 = 3λ at w 20 = -w 22/2. (b) Image of an off-axial point source formed by a compensating mask with α1 = 0°, α2 = 90°, a/ b = 1, δ = 90°, γ = 135° with w 22 = 3λ.

Fig. 6
Fig. 6

(a) Image of an off-axial point source formed by a clear aperture lens in the presence of astigmatism, w 22 = 5λ at w 20 = -w 22/2. (b) Image of an off-axial point source formed by a compensating mask with α1 = 0°, α2 = 90°, a/ b = 1, δ = 90°, γ = 135° with w 22 = 5λ.

Fig. 7
Fig. 7

(a) Image of an off-axial point source formed by a clear aperture lens in the presence of astigmatism, w 22 = 7λ at w 20 = -w 22/2. (b) Image of an off-axial point source formed by a compensating mask with α1 = 0°, α2 = 90°, a/ b = 1, δ = 90°, γ = 135° with w 22 = 7λ.

Fig. 8
Fig. 8

(a) Image of an off-axial point source formed by a clear aperture lens in the presence of astigmatism, w 22 = 9λ at w 20 = -w 22/2. (b) Image of an off-axial point source formed by a compensating mask with α1 = 0°, α2 = 90°, a/ b = 1, δ = 90°, γ = 135° with w 22 = 9λ.

Fig. 9
Fig. 9

Image of an off-axial point source formed by a compensating mask with α1 = 0°, α2 = 90°, a/ b = 1, δ = 90°, γ = 135° with w 22 = 3λ. The mask is rotated through 90° from that shown in Fig. 2.

Fig. 10
Fig. 10

Image of an off-axial point source formed by a compensating mask with α1 = 0°, α2 = 90°, a/ b = 1, δ = 180°, γ = 135° with w 22 = 3λ.

Fig. 11
Fig. 11

Image of an off-axial point source formed by a compensating mask with α1 = 0°, α2 = 90°, a/ b = 1, δ = 90°, γ = 60° with w 22 = 3λ.

Equations (10)

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

Iν, θ=R1R2ϕ1ϕ2 Tρ, θexpikWρ, θ×exp-iνρ cosθ-θρdρdθ2,
εi=ab expiδ,
Iν, θ=p=1N Tp expiΔp01ϕ1ϕ2expikWρ, θ×exp-iνρ cosθ-θρdρdθ2,
ϕ1=p-12πN,ϕ2=p 2πN,
Δp=tan-1b sin αp sin δa cos αp+b sin αp cos δ,
Tp=a2 cos2 αp+b2 sin2 αp+ab sin 2α cos δ1/2.
Tp=Tp cosγ-αp.
wρ, θ=w20ρ2+w22ρ2 cos2 θ,
ρ2=m,
Iν, θ=p=1N Tp expiΔp01ϕ1ϕ2expikmw20+w22 cos2 θexp-iνm1/2 cosθ-θdθdm.

Metrics