Abstract

A novel algorithm for the design of an imaging system that exhibits high resolution as well as extended depth of field is presented. This novel approach searches for an optimal pupil mask that minimizes the value of the mean-square error when performed over the intensity rather than in the field distribution of the acquired image. The captured images in such system do not require any postprocessing, and thus utilization of such a system is simplified. Simulations as well as experimental results are provided.

© 2006 Optical Society of America

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  1. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1996), pp. 126-151.
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  10. E. R. Dowski, Jr., and W. T. Cathey, "Extended depth of field through wave-front coding," Appl. Opt 34, 1859 (1995).
    [CrossRef] [PubMed]
  11. J. van der Gracht, E. R. Dowski, Jr., M. G. Taylor, and D. M. Deaver, "Broadband behavior of an optical-digital focus-invariant system," Opt. Lett. 21, 919-921 (1996).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
  14. N. George and W. Chi, "Computational imaging with the logarithmic asphere: theory," J. Opt. Soc. Am. A 20, 2260-2273 (2003).
    [CrossRef]
  15. S. Prasad, V. P. Pauca, R. J. Plemmons, T. C. Torgersen, and J. van der Gracht, "Pupil-phase optimization for extended focus, aberration corrected imaging systems," in Advanced Signal Processing Algorithms, Architectures, and Implementations XIV, F.T.Luck, E., Proc. SPIE 5559, 335-345 (2005).
  16. S. Prasad, T. C. Torgersen, V. P. Pauca, R. J. Plemmons, and J. van der Gracht, "High resolution imaging using integrated optical systems," Int. J. Imaging Syst. Technol. 14, 67-74 (2004).
    [CrossRef]
  17. J. van der Gracht, V. P. Pauca, H. Setty, R. Narayanswamy, R. Plemmons, S. Prasad, and T. Torgersen, "Iris recognition with enhanced depth-of-field image acquistion," in Visual Information Processing XIII, Z.Rahman, R.A.Schowengerdt, and S.E.Reichenbach, eds., Proc. SPIE 5438, 120-129 (2004).
  18. E. Ben-Eliezer, Z. Zalevsky, E. Marom, and N. Konforti, "All-optical extended depth of field imaging system," J. Opt. A Pure Appl. Opt. 5, S164-S169 (2003).
    [CrossRef]
  19. E. Ben-Eliezer, Z. Zalevsky, E. Marom, and N. Konforti, "All-optical extended depth of field imaging system," in 19th Congress of the International Commission for Optics: Optics for the Quality of Life, G.C.Righini and A.Consortini, eds., Proc. SPIE 4829, 221-222 (2002).
  20. E. Ben-Eliezer, Z. Zalevsky, E. Marom, and N. Konforti, "Experimental realization of an imaging system with an extended depth of field," Appl. Opt. 44, 2792-2798 (2005).
    [CrossRef] [PubMed]
  21. S. Kirkpatrick, C. D. Gelatt, and M. P. Vecchi, "Optimization by simulated annealing," Science 220, 671-680 (1983).
    [CrossRef] [PubMed]
  22. M. Nieto-Vesperinas, R. Navarro, and F. J. Fuentes, "Performance of simulated annealing algorithm for phase retrival," J. Opt. Soc. Am. A 5, 30-38 (1988).
    [CrossRef]
  23. H. Szu and R. Hartley, "Fast simulated annealing," Phys. Lett. A 122, 157-162 (1987).
    [CrossRef]

2005 (1)

2004 (2)

S. Sherif, W. T. Cathey, and E. R. Dowski, "Phase plate to extend the depth of field of incoherent hybrid imaging systems," Appl. Opt. 43, 2709-2721 (2004).
[CrossRef] [PubMed]

S. Prasad, T. C. Torgersen, V. P. Pauca, R. J. Plemmons, and J. van der Gracht, "High resolution imaging using integrated optical systems," Int. J. Imaging Syst. Technol. 14, 67-74 (2004).
[CrossRef]

2003 (2)

E. Ben-Eliezer, Z. Zalevsky, E. Marom, and N. Konforti, "All-optical extended depth of field imaging system," J. Opt. A Pure Appl. Opt. 5, S164-S169 (2003).
[CrossRef]

N. George and W. Chi, "Computational imaging with the logarithmic asphere: theory," J. Opt. Soc. Am. A 20, 2260-2273 (2003).
[CrossRef]

2001 (2)

E. Peli and A. Lang, "Appearance of images through a multifocal intraocular lens," J. Opt. Soc. Am. A 18, 302-309 (2001).
[CrossRef]

W. Chi and N. George, "Electronic imaging using a logarithmic asphere," Opt. Lett , 26, 875-877 (2001).
[CrossRef]

2000 (1)

1997 (1)

1996 (1)

1995 (1)

E. R. Dowski, Jr., and W. T. Cathey, "Extended depth of field through wave-front coding," Appl. Opt 34, 1859 (1995).
[CrossRef] [PubMed]

1990 (1)

1989 (1)

1988 (2)

1987 (2)

1983 (1)

S. Kirkpatrick, C. D. Gelatt, and M. P. Vecchi, "Optimization by simulated annealing," Science 220, 671-680 (1983).
[CrossRef] [PubMed]

1971 (1)

Ben-Eliezer, E.

E. Ben-Eliezer, Z. Zalevsky, E. Marom, and N. Konforti, "Experimental realization of an imaging system with an extended depth of field," Appl. Opt. 44, 2792-2798 (2005).
[CrossRef] [PubMed]

E. Ben-Eliezer, Z. Zalevsky, E. Marom, and N. Konforti, "All-optical extended depth of field imaging system," J. Opt. A Pure Appl. Opt. 5, S164-S169 (2003).
[CrossRef]

E. Ben-Eliezer, Z. Zalevsky, E. Marom, and N. Konforti, "All-optical extended depth of field imaging system," in 19th Congress of the International Commission for Optics: Optics for the Quality of Life, G.C.Righini and A.Consortini, eds., Proc. SPIE 4829, 221-222 (2002).

Berriel-Valdos, L. R.

Castaneda, J. O.

Cathey, W. T.

Chi, W.

N. George and W. Chi, "Computational imaging with the logarithmic asphere: theory," J. Opt. Soc. Am. A 20, 2260-2273 (2003).
[CrossRef]

W. Chi and N. George, "Electronic imaging using a logarithmic asphere," Opt. Lett , 26, 875-877 (2001).
[CrossRef]

Deaver, D. M.

Diaz, A.

Dowski, E. R.

Fuentes, F. J.

Gelatt, C. D.

S. Kirkpatrick, C. D. Gelatt, and M. P. Vecchi, "Optimization by simulated annealing," Science 220, 671-680 (1983).
[CrossRef] [PubMed]

George, N.

N. George and W. Chi, "Computational imaging with the logarithmic asphere: theory," J. Opt. Soc. Am. A 20, 2260-2273 (2003).
[CrossRef]

W. Chi and N. George, "Electronic imaging using a logarithmic asphere," Opt. Lett , 26, 875-877 (2001).
[CrossRef]

Ghosh, A.

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1996), pp. 126-151.

Hartley, R.

H. Szu and R. Hartley, "Fast simulated annealing," Phys. Lett. A 122, 157-162 (1987).
[CrossRef]

Kirkpatrick, S.

S. Kirkpatrick, C. D. Gelatt, and M. P. Vecchi, "Optimization by simulated annealing," Science 220, 671-680 (1983).
[CrossRef] [PubMed]

Konforti, N.

E. Ben-Eliezer, Z. Zalevsky, E. Marom, and N. Konforti, "Experimental realization of an imaging system with an extended depth of field," Appl. Opt. 44, 2792-2798 (2005).
[CrossRef] [PubMed]

E. Ben-Eliezer, Z. Zalevsky, E. Marom, and N. Konforti, "All-optical extended depth of field imaging system," J. Opt. A Pure Appl. Opt. 5, S164-S169 (2003).
[CrossRef]

E. Ben-Eliezer, Z. Zalevsky, E. Marom, and N. Konforti, "All-optical extended depth of field imaging system," in 19th Congress of the International Commission for Optics: Optics for the Quality of Life, G.C.Righini and A.Consortini, eds., Proc. SPIE 4829, 221-222 (2002).

Lang, A.

Lohmann, A. W.

Marom, E.

E. Ben-Eliezer, Z. Zalevsky, E. Marom, and N. Konforti, "Experimental realization of an imaging system with an extended depth of field," Appl. Opt. 44, 2792-2798 (2005).
[CrossRef] [PubMed]

E. Ben-Eliezer, Z. Zalevsky, E. Marom, and N. Konforti, "All-optical extended depth of field imaging system," J. Opt. A Pure Appl. Opt. 5, S164-S169 (2003).
[CrossRef]

E. Ben-Eliezer, Z. Zalevsky, E. Marom, and N. Konforti, "All-optical extended depth of field imaging system," in 19th Congress of the International Commission for Optics: Optics for the Quality of Life, G.C.Righini and A.Consortini, eds., Proc. SPIE 4829, 221-222 (2002).

Mendlovic, D.

Mino, M.

Motamedi, M.

Narayanswamy, R.

J. van der Gracht, V. P. Pauca, H. Setty, R. Narayanswamy, R. Plemmons, S. Prasad, and T. Torgersen, "Iris recognition with enhanced depth-of-field image acquistion," in Visual Information Processing XIII, Z.Rahman, R.A.Schowengerdt, and S.E.Reichenbach, eds., Proc. SPIE 5438, 120-129 (2004).

Navarro, R.

Nieto-Vesperinas, M.

Noyola-Isgleas, A.

Okano, Y.

Pauca, V. P.

S. Prasad, T. C. Torgersen, V. P. Pauca, R. J. Plemmons, and J. van der Gracht, "High resolution imaging using integrated optical systems," Int. J. Imaging Syst. Technol. 14, 67-74 (2004).
[CrossRef]

J. van der Gracht, V. P. Pauca, H. Setty, R. Narayanswamy, R. Plemmons, S. Prasad, and T. Torgersen, "Iris recognition with enhanced depth-of-field image acquistion," in Visual Information Processing XIII, Z.Rahman, R.A.Schowengerdt, and S.E.Reichenbach, eds., Proc. SPIE 5438, 120-129 (2004).

S. Prasad, V. P. Pauca, R. J. Plemmons, T. C. Torgersen, and J. van der Gracht, "Pupil-phase optimization for extended focus, aberration corrected imaging systems," in Advanced Signal Processing Algorithms, Architectures, and Implementations XIV, F.T.Luck, E., Proc. SPIE 5559, 335-345 (2005).

Peli, E.

Plemmons, R.

J. van der Gracht, V. P. Pauca, H. Setty, R. Narayanswamy, R. Plemmons, S. Prasad, and T. Torgersen, "Iris recognition with enhanced depth-of-field image acquistion," in Visual Information Processing XIII, Z.Rahman, R.A.Schowengerdt, and S.E.Reichenbach, eds., Proc. SPIE 5438, 120-129 (2004).

Plemmons, R. J.

S. Prasad, T. C. Torgersen, V. P. Pauca, R. J. Plemmons, and J. van der Gracht, "High resolution imaging using integrated optical systems," Int. J. Imaging Syst. Technol. 14, 67-74 (2004).
[CrossRef]

S. Prasad, V. P. Pauca, R. J. Plemmons, T. C. Torgersen, and J. van der Gracht, "Pupil-phase optimization for extended focus, aberration corrected imaging systems," in Advanced Signal Processing Algorithms, Architectures, and Implementations XIV, F.T.Luck, E., Proc. SPIE 5559, 335-345 (2005).

Poon, T. C.

Prasad, S.

S. Prasad, T. C. Torgersen, V. P. Pauca, R. J. Plemmons, and J. van der Gracht, "High resolution imaging using integrated optical systems," Int. J. Imaging Syst. Technol. 14, 67-74 (2004).
[CrossRef]

S. Prasad, V. P. Pauca, R. J. Plemmons, T. C. Torgersen, and J. van der Gracht, "Pupil-phase optimization for extended focus, aberration corrected imaging systems," in Advanced Signal Processing Algorithms, Architectures, and Implementations XIV, F.T.Luck, E., Proc. SPIE 5559, 335-345 (2005).

J. van der Gracht, V. P. Pauca, H. Setty, R. Narayanswamy, R. Plemmons, S. Prasad, and T. Torgersen, "Iris recognition with enhanced depth-of-field image acquistion," in Visual Information Processing XIII, Z.Rahman, R.A.Schowengerdt, and S.E.Reichenbach, eds., Proc. SPIE 5438, 120-129 (2004).

Ramos, R.

Sanyal, S.

Setty, H.

J. van der Gracht, V. P. Pauca, H. Setty, R. Narayanswamy, R. Plemmons, S. Prasad, and T. Torgersen, "Iris recognition with enhanced depth-of-field image acquistion," in Visual Information Processing XIII, Z.Rahman, R.A.Schowengerdt, and S.E.Reichenbach, eds., Proc. SPIE 5438, 120-129 (2004).

Sherif, S.

Szu, H.

H. Szu and R. Hartley, "Fast simulated annealing," Phys. Lett. A 122, 157-162 (1987).
[CrossRef]

Taylor, M. G.

Tepichin, E.

Torgersen, T.

J. van der Gracht, V. P. Pauca, H. Setty, R. Narayanswamy, R. Plemmons, S. Prasad, and T. Torgersen, "Iris recognition with enhanced depth-of-field image acquistion," in Visual Information Processing XIII, Z.Rahman, R.A.Schowengerdt, and S.E.Reichenbach, eds., Proc. SPIE 5438, 120-129 (2004).

Torgersen, T. C.

S. Prasad, T. C. Torgersen, V. P. Pauca, R. J. Plemmons, and J. van der Gracht, "High resolution imaging using integrated optical systems," Int. J. Imaging Syst. Technol. 14, 67-74 (2004).
[CrossRef]

S. Prasad, V. P. Pauca, R. J. Plemmons, T. C. Torgersen, and J. van der Gracht, "Pupil-phase optimization for extended focus, aberration corrected imaging systems," in Advanced Signal Processing Algorithms, Architectures, and Implementations XIV, F.T.Luck, E., Proc. SPIE 5559, 335-345 (2005).

van der Gracht, J.

S. Prasad, T. C. Torgersen, V. P. Pauca, R. J. Plemmons, and J. van der Gracht, "High resolution imaging using integrated optical systems," Int. J. Imaging Syst. Technol. 14, 67-74 (2004).
[CrossRef]

J. van der Gracht, E. R. Dowski, Jr., M. G. Taylor, and D. M. Deaver, "Broadband behavior of an optical-digital focus-invariant system," Opt. Lett. 21, 919-921 (1996).
[CrossRef] [PubMed]

S. Prasad, V. P. Pauca, R. J. Plemmons, T. C. Torgersen, and J. van der Gracht, "Pupil-phase optimization for extended focus, aberration corrected imaging systems," in Advanced Signal Processing Algorithms, Architectures, and Implementations XIV, F.T.Luck, E., Proc. SPIE 5559, 335-345 (2005).

J. van der Gracht, V. P. Pauca, H. Setty, R. Narayanswamy, R. Plemmons, S. Prasad, and T. Torgersen, "Iris recognition with enhanced depth-of-field image acquistion," in Visual Information Processing XIII, Z.Rahman, R.A.Schowengerdt, and S.E.Reichenbach, eds., Proc. SPIE 5438, 120-129 (2004).

Vecchi, M. P.

S. Kirkpatrick, C. D. Gelatt, and M. P. Vecchi, "Optimization by simulated annealing," Science 220, 671-680 (1983).
[CrossRef] [PubMed]

Zalevsky, Z.

E. Ben-Eliezer, Z. Zalevsky, E. Marom, and N. Konforti, "Experimental realization of an imaging system with an extended depth of field," Appl. Opt. 44, 2792-2798 (2005).
[CrossRef] [PubMed]

E. Ben-Eliezer, Z. Zalevsky, E. Marom, and N. Konforti, "All-optical extended depth of field imaging system," J. Opt. A Pure Appl. Opt. 5, S164-S169 (2003).
[CrossRef]

A. W. Lohmann, D. Mendlovic, and Z. Zalevsky, "Digital method for measuring the focus error," Appl. Opt. 36, 7204-7209 (1997).
[CrossRef]

E. Ben-Eliezer, Z. Zalevsky, E. Marom, and N. Konforti, "All-optical extended depth of field imaging system," in 19th Congress of the International Commission for Optics: Optics for the Quality of Life, G.C.Righini and A.Consortini, eds., Proc. SPIE 4829, 221-222 (2002).

Appl. Opt (1)

E. R. Dowski, Jr., and W. T. Cathey, "Extended depth of field through wave-front coding," Appl. Opt 34, 1859 (1995).
[CrossRef] [PubMed]

Appl. Opt. (9)

Int. J. Imaging Syst. Technol. (1)

S. Prasad, T. C. Torgersen, V. P. Pauca, R. J. Plemmons, and J. van der Gracht, "High resolution imaging using integrated optical systems," Int. J. Imaging Syst. Technol. 14, 67-74 (2004).
[CrossRef]

J. Opt. A Pure Appl. Opt. (1)

E. Ben-Eliezer, Z. Zalevsky, E. Marom, and N. Konforti, "All-optical extended depth of field imaging system," J. Opt. A Pure Appl. Opt. 5, S164-S169 (2003).
[CrossRef]

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

Opt. Lett (1)

W. Chi and N. George, "Electronic imaging using a logarithmic asphere," Opt. Lett , 26, 875-877 (2001).
[CrossRef]

Opt. Lett. (1)

Phys. Lett. A (1)

H. Szu and R. Hartley, "Fast simulated annealing," Phys. Lett. A 122, 157-162 (1987).
[CrossRef]

Science (1)

S. Kirkpatrick, C. D. Gelatt, and M. P. Vecchi, "Optimization by simulated annealing," Science 220, 671-680 (1983).
[CrossRef] [PubMed]

Other (4)

E. Ben-Eliezer, Z. Zalevsky, E. Marom, and N. Konforti, "All-optical extended depth of field imaging system," in 19th Congress of the International Commission for Optics: Optics for the Quality of Life, G.C.Righini and A.Consortini, eds., Proc. SPIE 4829, 221-222 (2002).

J. van der Gracht, V. P. Pauca, H. Setty, R. Narayanswamy, R. Plemmons, S. Prasad, and T. Torgersen, "Iris recognition with enhanced depth-of-field image acquistion," in Visual Information Processing XIII, Z.Rahman, R.A.Schowengerdt, and S.E.Reichenbach, eds., Proc. SPIE 5438, 120-129 (2004).

S. Prasad, V. P. Pauca, R. J. Plemmons, T. C. Torgersen, and J. van der Gracht, "Pupil-phase optimization for extended focus, aberration corrected imaging systems," in Advanced Signal Processing Algorithms, Architectures, and Implementations XIV, F.T.Luck, E., Proc. SPIE 5559, 335-345 (2005).

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1996), pp. 126-151.

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Figures (14)

Fig. 1
Fig. 1

Desired OTF curves used for simulated annealing iterations: solid curve, triangular diffraction-limited OTF; dashed curve, contrast-reduced OTF. The incoherent normalized cutoff frequency is 2.

Fig. 2
Fig. 2

Weight function used for the simulations. The incoherent normalized cutoff frequency is 2.

Fig. 3
Fig. 3

Left, MTF and right, phase of the OTF of the 1D pupil mask calculated for the aberration-free (triangular) desired OTF: (a) ψ = 0, (b) ψ = 12, (c) ψ = 14. The incoherent normalized cutoff frequency is 2.

Fig. 4
Fig. 4

Experimental setup: (a) monochromatic illumination, (b) polychromatic illumination.

Fig. 5
Fig. 5

Left, MTF and right, phase of the OTF of the 1D pupil mask calculated for the contrast-reduced desired OTF and W(v) as in Fig. 2: (a) ψ = 0, (b) ψ = 12, (c) ψ = 14. The incoherent normalized cutoff frequency is 2.

Fig. 6
Fig. 6

Resultant optimal pupil masks: left, amplitude value and right, its phase. (a) Mask obtained for aberration-free (triangular) desired OTF, (b) mask obtained for contrast-reduced desired OTF desired OTF with W(v) as in Fig. 2.

Fig. 7
Fig. 7

Amplitude and phase of radial masks: (a) Direct optimization of a two-dimensional radial mask; (b) mask obtained by azimuthal averaging of the product of two 1D distributions, based on the diffraction-limited desired OTF; (c) same as (b) but with the contrast-reduced OTF and W(v) as provided in Fig. 2.

Fig. 8
Fig. 8

MTF cross-section results. Top, MTF curves of the optimal radial mask; middle, MTF curves for the suboptimal radial mask obtained with the triangular 1D desired OTF; bottom, MTF curves for the suboptimal radial mask obtained with the contrast-reduced 1D desired OTF and W(v) as in Fig. 2. Left, object in the focus position; center, object in the misfocus position corresponding to ψ = 12; right, object in the misfocus position corresponding to ψ = 15. The incoherent normalized cutoff frequency is 2.

Fig. 9
Fig. 9

Comparison of clear aperture (solid curve), and mask-equipped aperture (dashed curves) MTFs for the in-focus condition and the same light throughout: (a) optimal 1D, (b) radial case. The normalized cutoff frequency is 2.

Fig. 10
Fig. 10

MTF cross-section curves for (a1)–(a3) a clear aperture and (b1)–(b3) the phase-only mask. Misfocus conditions ψ = 0 (perfect focus), middle, ψ = 12, bottom, ψ = 15. The incoherent normalized cutoff frequency is 2.

Fig. 11
Fig. 11

Images for monochromatic illumination acquired with the clear aperture for top, in-focus position and bottom, the misfocus condition of ψ = 15.

Fig. 12
Fig. 12

Images for monochromatic illumination acquired with the radial phase-only mask for top, the in-focus position and bottom, the misfocus condition of ψ = 15.

Fig. 13
Fig. 13

Images for polychromatic illumination acquired with a clear aperture for top, the in-focus position and bottom, the misfocus condition of ψ = 15 (calculated for λ = 632.8 nm).

Fig. 14
Fig. 14

Images for polychromatic illumination with the radial phase-only mask for top, the in-focus position and bottom, the misfocus condition of ψ = 15 (calculated for λ = 632.8 nm).

Equations (13)

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

G ( u , v ; ψ ) = exp [ j ψ ( u 2 + v 2 ) ] ,
ψ = π L 2 4 λ ( 1 d obj + 1 d img 1 f ) ,
P ˜ ( u , v ) = P ( u , v ) exp [ j ψ ( u 2 + v 2 ) ] ,
I out ( x , y ) = | h ( x x , y y ) | 2 I g ( x , y ) d x d y ,
E 2 = | h ( x , y , ψ ) h d ( x , y ) | 2  d x d y d ψ ,
E 2 = ( | h ( x , y ; ψ ) | 2 | h d ( x , y ) | 2 ) 2  d x d y d ψ .
E 2 = | OTF ( v x , v y ; ψ ) OTF d ( v x , v y ) | 2  d v x d v y d ψ ,
Pr { E = E } = A exp ( E k b T ) ,
Δ i , i 1 = C i ( u ¯ i ) C i 1 ( u ¯ i 1 ) .
r exp ( Δ i , i 1 / T )  accept,
r > exp ( Δ i , i 1 / T )   reject,
E 2 = W ( v x , v y ) | OTF ( v x , v y ; ψ ) OTF d ( v x , v y ) | 2  d v x d v y dψ,
M ( r ) = 1 2 π α α + 2 π M sep ( r , θ ) d θ ,

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