Abstract

We propose a method to reduce the color moire fringes that are attributable to the structure of a color flat-panel display in integral three-dimensional imaging. The method uses two types of optical low-pass filter, diffuser and defocus. The effectiveness of the method was confirmed in an experiment. We describe a way to design these filters with moire’s residual energy and video signal energy as indices and demonstrate the validity of the model, which combines two filters to reduce moire fringes.

© 2005 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. A. Schmidt, A. Grasnick, “Multiviewpoint autostereoscopic displays from 4D vision,” in Stereoscopic Displays and Virtual Reality Systems XI,A. J. Woods, J. O. Merritt, S. A. Benton, M. T. Bolas, eds., Proc. SPIE4660, 212–221 (2002).
    [CrossRef]
  2. L. Lipton, M. Feldman, “A new autostereoscopic display technology: the SynthaGram,” in Stereoscopic Displays and Virtual Reality Systems XI,A. J. Woods, J. O. Merritt, S. A. Benton, M. T. Bolas, eds., Proc. SPIE4660, 229–235 (2002).
    [CrossRef]
  3. K. Mashitani, G. Hamagishi, M. Higashino, T. Ando, S. Takemoto, “Step barrier system multiview glassless 3D display,” in Stereoscopic Displays and Virtual Reality Systems XI,A. J. Woods, J. O. Merritt, S. A. Benton, M. T. Bolas, eds., Proc. SPIE5291, 265–272 (2004).
    [CrossRef]
  4. M. McCormick, “Integral 3-D imaging for broadcast,” in Proceedings of the 2nd International Display Workshops, (Institute of Image Information and Television Engineers of Japan, 1995), Vol. 3, pp. 77–80.
  5. F. Okano, H. Hoshino, J. Arai, I. Yuyama, “Real-time pickup method for a three-dimensional image based on integral photography,” Appl. Opt. 36, 1598–1603 (1997).
    [CrossRef] [PubMed]
  6. H. Hoshino, F. Okano, H. Isono, I. Yuyama, “Analysis of resolution limitation of integral photography,” J. Opt. Soc. Am. A 15, 2059–2065 (1998).
    [CrossRef]
  7. M. Sawahata, S. Mikoshiba, S. Shirai, K. Oshita, “Tailring of an electron beam shape for reduction of CRT moire fringes,” in Proceedings of the 3rd International Display Workshops (Society of Information Display, 1996), Vol. 2, pp. 221–224.
  8. R. Börner, “Four autostereoscopic monitors on the level of industrial prototypes,” Displays 20, 57–64 (1999).
    [CrossRef]
  9. J.-Y. Son, V. Saveljev, S.-H. Shin, Y.-J. Choi, S.-S. Kim, “Moire pattern reduction in full-parallax autostereoscopic imaging systems using two crossed lenticular plates as a viewing zone forming optics,” in Proceedings of the 10th International Display Workshops (Institute of Image Information and Television Engineers of Japan, and Society of Information Display, 2003), pp. 1401–1404.
  10. M. Okui, M. Kobayashi, J. Arai, T. Mishina, F. Okano, “3-D display system,” Japanese patent application laid-open disclosure number JP 2004-118140 A (15April2004).
  11. F. Okano, J. Arai, H. Hoshino, I. Yuyama, “Three-dimensional video system based on integral photography,” Opt. Eng. 38, 1072–1077 (1997).
    [CrossRef]
  12. G. Lippmann, C. R. Acad. Sci. 146, 446–451 (1908).
  13. M. Kanazawa, K. Hamada, F. Okano, “Color error from an RGB-strip pixel structure,” J. Soc. Inf. Display 11(2), 387–393 (2003).
    [CrossRef]
  14. J. Petersen, J. Lerner, “Homogenizer formed using coherent light and a holographic diffuser,” U.S. patent5,534,386 (9July1996).
  15. M. Kobayashi, J. Arai, M. Okui, F. Okano, “Moire reducing method for integral photography display,” (Institute of Image Information and Television Engineers of Japan, 2002), Vol. 26, No. 74 (in Japanese).
  16. J. Arai, H. Hoshino, M. Okui, F. Okano, “Effects of focusing on the resolution characteristics of integral photography,” J. Opt. Soc. Am. A 20, 996–1004 (2003).
    [CrossRef]

2003

M. Kanazawa, K. Hamada, F. Okano, “Color error from an RGB-strip pixel structure,” J. Soc. Inf. Display 11(2), 387–393 (2003).
[CrossRef]

J. Arai, H. Hoshino, M. Okui, F. Okano, “Effects of focusing on the resolution characteristics of integral photography,” J. Opt. Soc. Am. A 20, 996–1004 (2003).
[CrossRef]

1999

R. Börner, “Four autostereoscopic monitors on the level of industrial prototypes,” Displays 20, 57–64 (1999).
[CrossRef]

1998

1997

F. Okano, H. Hoshino, J. Arai, I. Yuyama, “Real-time pickup method for a three-dimensional image based on integral photography,” Appl. Opt. 36, 1598–1603 (1997).
[CrossRef] [PubMed]

F. Okano, J. Arai, H. Hoshino, I. Yuyama, “Three-dimensional video system based on integral photography,” Opt. Eng. 38, 1072–1077 (1997).
[CrossRef]

1908

G. Lippmann, C. R. Acad. Sci. 146, 446–451 (1908).

Ando, T.

K. Mashitani, G. Hamagishi, M. Higashino, T. Ando, S. Takemoto, “Step barrier system multiview glassless 3D display,” in Stereoscopic Displays and Virtual Reality Systems XI,A. J. Woods, J. O. Merritt, S. A. Benton, M. T. Bolas, eds., Proc. SPIE5291, 265–272 (2004).
[CrossRef]

Arai, J.

J. Arai, H. Hoshino, M. Okui, F. Okano, “Effects of focusing on the resolution characteristics of integral photography,” J. Opt. Soc. Am. A 20, 996–1004 (2003).
[CrossRef]

F. Okano, J. Arai, H. Hoshino, I. Yuyama, “Three-dimensional video system based on integral photography,” Opt. Eng. 38, 1072–1077 (1997).
[CrossRef]

F. Okano, H. Hoshino, J. Arai, I. Yuyama, “Real-time pickup method for a three-dimensional image based on integral photography,” Appl. Opt. 36, 1598–1603 (1997).
[CrossRef] [PubMed]

M. Okui, M. Kobayashi, J. Arai, T. Mishina, F. Okano, “3-D display system,” Japanese patent application laid-open disclosure number JP 2004-118140 A (15April2004).

M. Kobayashi, J. Arai, M. Okui, F. Okano, “Moire reducing method for integral photography display,” (Institute of Image Information and Television Engineers of Japan, 2002), Vol. 26, No. 74 (in Japanese).

Börner, R.

R. Börner, “Four autostereoscopic monitors on the level of industrial prototypes,” Displays 20, 57–64 (1999).
[CrossRef]

Choi, Y.-J.

J.-Y. Son, V. Saveljev, S.-H. Shin, Y.-J. Choi, S.-S. Kim, “Moire pattern reduction in full-parallax autostereoscopic imaging systems using two crossed lenticular plates as a viewing zone forming optics,” in Proceedings of the 10th International Display Workshops (Institute of Image Information and Television Engineers of Japan, and Society of Information Display, 2003), pp. 1401–1404.

Feldman, M.

L. Lipton, M. Feldman, “A new autostereoscopic display technology: the SynthaGram,” in Stereoscopic Displays and Virtual Reality Systems XI,A. J. Woods, J. O. Merritt, S. A. Benton, M. T. Bolas, eds., Proc. SPIE4660, 229–235 (2002).
[CrossRef]

Grasnick, A.

A. Schmidt, A. Grasnick, “Multiviewpoint autostereoscopic displays from 4D vision,” in Stereoscopic Displays and Virtual Reality Systems XI,A. J. Woods, J. O. Merritt, S. A. Benton, M. T. Bolas, eds., Proc. SPIE4660, 212–221 (2002).
[CrossRef]

Hamada, K.

M. Kanazawa, K. Hamada, F. Okano, “Color error from an RGB-strip pixel structure,” J. Soc. Inf. Display 11(2), 387–393 (2003).
[CrossRef]

Hamagishi, G.

K. Mashitani, G. Hamagishi, M. Higashino, T. Ando, S. Takemoto, “Step barrier system multiview glassless 3D display,” in Stereoscopic Displays and Virtual Reality Systems XI,A. J. Woods, J. O. Merritt, S. A. Benton, M. T. Bolas, eds., Proc. SPIE5291, 265–272 (2004).
[CrossRef]

Higashino, M.

K. Mashitani, G. Hamagishi, M. Higashino, T. Ando, S. Takemoto, “Step barrier system multiview glassless 3D display,” in Stereoscopic Displays and Virtual Reality Systems XI,A. J. Woods, J. O. Merritt, S. A. Benton, M. T. Bolas, eds., Proc. SPIE5291, 265–272 (2004).
[CrossRef]

Hoshino, H.

Isono, H.

Kanazawa, M.

M. Kanazawa, K. Hamada, F. Okano, “Color error from an RGB-strip pixel structure,” J. Soc. Inf. Display 11(2), 387–393 (2003).
[CrossRef]

Kim, S.-S.

J.-Y. Son, V. Saveljev, S.-H. Shin, Y.-J. Choi, S.-S. Kim, “Moire pattern reduction in full-parallax autostereoscopic imaging systems using two crossed lenticular plates as a viewing zone forming optics,” in Proceedings of the 10th International Display Workshops (Institute of Image Information and Television Engineers of Japan, and Society of Information Display, 2003), pp. 1401–1404.

Kobayashi, M.

M. Okui, M. Kobayashi, J. Arai, T. Mishina, F. Okano, “3-D display system,” Japanese patent application laid-open disclosure number JP 2004-118140 A (15April2004).

M. Kobayashi, J. Arai, M. Okui, F. Okano, “Moire reducing method for integral photography display,” (Institute of Image Information and Television Engineers of Japan, 2002), Vol. 26, No. 74 (in Japanese).

Lerner, J.

J. Petersen, J. Lerner, “Homogenizer formed using coherent light and a holographic diffuser,” U.S. patent5,534,386 (9July1996).

Lippmann, G.

G. Lippmann, C. R. Acad. Sci. 146, 446–451 (1908).

Lipton, L.

L. Lipton, M. Feldman, “A new autostereoscopic display technology: the SynthaGram,” in Stereoscopic Displays and Virtual Reality Systems XI,A. J. Woods, J. O. Merritt, S. A. Benton, M. T. Bolas, eds., Proc. SPIE4660, 229–235 (2002).
[CrossRef]

Mashitani, K.

K. Mashitani, G. Hamagishi, M. Higashino, T. Ando, S. Takemoto, “Step barrier system multiview glassless 3D display,” in Stereoscopic Displays and Virtual Reality Systems XI,A. J. Woods, J. O. Merritt, S. A. Benton, M. T. Bolas, eds., Proc. SPIE5291, 265–272 (2004).
[CrossRef]

McCormick, M.

M. McCormick, “Integral 3-D imaging for broadcast,” in Proceedings of the 2nd International Display Workshops, (Institute of Image Information and Television Engineers of Japan, 1995), Vol. 3, pp. 77–80.

Mikoshiba, S.

M. Sawahata, S. Mikoshiba, S. Shirai, K. Oshita, “Tailring of an electron beam shape for reduction of CRT moire fringes,” in Proceedings of the 3rd International Display Workshops (Society of Information Display, 1996), Vol. 2, pp. 221–224.

Mishina, T.

M. Okui, M. Kobayashi, J. Arai, T. Mishina, F. Okano, “3-D display system,” Japanese patent application laid-open disclosure number JP 2004-118140 A (15April2004).

Okano, F.

M. Kanazawa, K. Hamada, F. Okano, “Color error from an RGB-strip pixel structure,” J. Soc. Inf. Display 11(2), 387–393 (2003).
[CrossRef]

J. Arai, H. Hoshino, M. Okui, F. Okano, “Effects of focusing on the resolution characteristics of integral photography,” J. Opt. Soc. Am. A 20, 996–1004 (2003).
[CrossRef]

H. Hoshino, F. Okano, H. Isono, I. Yuyama, “Analysis of resolution limitation of integral photography,” J. Opt. Soc. Am. A 15, 2059–2065 (1998).
[CrossRef]

F. Okano, H. Hoshino, J. Arai, I. Yuyama, “Real-time pickup method for a three-dimensional image based on integral photography,” Appl. Opt. 36, 1598–1603 (1997).
[CrossRef] [PubMed]

F. Okano, J. Arai, H. Hoshino, I. Yuyama, “Three-dimensional video system based on integral photography,” Opt. Eng. 38, 1072–1077 (1997).
[CrossRef]

M. Okui, M. Kobayashi, J. Arai, T. Mishina, F. Okano, “3-D display system,” Japanese patent application laid-open disclosure number JP 2004-118140 A (15April2004).

M. Kobayashi, J. Arai, M. Okui, F. Okano, “Moire reducing method for integral photography display,” (Institute of Image Information and Television Engineers of Japan, 2002), Vol. 26, No. 74 (in Japanese).

Okui, M.

J. Arai, H. Hoshino, M. Okui, F. Okano, “Effects of focusing on the resolution characteristics of integral photography,” J. Opt. Soc. Am. A 20, 996–1004 (2003).
[CrossRef]

M. Kobayashi, J. Arai, M. Okui, F. Okano, “Moire reducing method for integral photography display,” (Institute of Image Information and Television Engineers of Japan, 2002), Vol. 26, No. 74 (in Japanese).

M. Okui, M. Kobayashi, J. Arai, T. Mishina, F. Okano, “3-D display system,” Japanese patent application laid-open disclosure number JP 2004-118140 A (15April2004).

Oshita, K.

M. Sawahata, S. Mikoshiba, S. Shirai, K. Oshita, “Tailring of an electron beam shape for reduction of CRT moire fringes,” in Proceedings of the 3rd International Display Workshops (Society of Information Display, 1996), Vol. 2, pp. 221–224.

Petersen, J.

J. Petersen, J. Lerner, “Homogenizer formed using coherent light and a holographic diffuser,” U.S. patent5,534,386 (9July1996).

Saveljev, V.

J.-Y. Son, V. Saveljev, S.-H. Shin, Y.-J. Choi, S.-S. Kim, “Moire pattern reduction in full-parallax autostereoscopic imaging systems using two crossed lenticular plates as a viewing zone forming optics,” in Proceedings of the 10th International Display Workshops (Institute of Image Information and Television Engineers of Japan, and Society of Information Display, 2003), pp. 1401–1404.

Sawahata, M.

M. Sawahata, S. Mikoshiba, S. Shirai, K. Oshita, “Tailring of an electron beam shape for reduction of CRT moire fringes,” in Proceedings of the 3rd International Display Workshops (Society of Information Display, 1996), Vol. 2, pp. 221–224.

Schmidt, A.

A. Schmidt, A. Grasnick, “Multiviewpoint autostereoscopic displays from 4D vision,” in Stereoscopic Displays and Virtual Reality Systems XI,A. J. Woods, J. O. Merritt, S. A. Benton, M. T. Bolas, eds., Proc. SPIE4660, 212–221 (2002).
[CrossRef]

Shin, S.-H.

J.-Y. Son, V. Saveljev, S.-H. Shin, Y.-J. Choi, S.-S. Kim, “Moire pattern reduction in full-parallax autostereoscopic imaging systems using two crossed lenticular plates as a viewing zone forming optics,” in Proceedings of the 10th International Display Workshops (Institute of Image Information and Television Engineers of Japan, and Society of Information Display, 2003), pp. 1401–1404.

Shirai, S.

M. Sawahata, S. Mikoshiba, S. Shirai, K. Oshita, “Tailring of an electron beam shape for reduction of CRT moire fringes,” in Proceedings of the 3rd International Display Workshops (Society of Information Display, 1996), Vol. 2, pp. 221–224.

Son, J.-Y.

J.-Y. Son, V. Saveljev, S.-H. Shin, Y.-J. Choi, S.-S. Kim, “Moire pattern reduction in full-parallax autostereoscopic imaging systems using two crossed lenticular plates as a viewing zone forming optics,” in Proceedings of the 10th International Display Workshops (Institute of Image Information and Television Engineers of Japan, and Society of Information Display, 2003), pp. 1401–1404.

Takemoto, S.

K. Mashitani, G. Hamagishi, M. Higashino, T. Ando, S. Takemoto, “Step barrier system multiview glassless 3D display,” in Stereoscopic Displays and Virtual Reality Systems XI,A. J. Woods, J. O. Merritt, S. A. Benton, M. T. Bolas, eds., Proc. SPIE5291, 265–272 (2004).
[CrossRef]

Yuyama, I.

Appl. Opt.

C. R. Acad. Sci.

G. Lippmann, C. R. Acad. Sci. 146, 446–451 (1908).

Displays

R. Börner, “Four autostereoscopic monitors on the level of industrial prototypes,” Displays 20, 57–64 (1999).
[CrossRef]

J. Opt. Soc. Am. A

J. Soc. Inf. Display

M. Kanazawa, K. Hamada, F. Okano, “Color error from an RGB-strip pixel structure,” J. Soc. Inf. Display 11(2), 387–393 (2003).
[CrossRef]

Opt. Eng.

F. Okano, J. Arai, H. Hoshino, I. Yuyama, “Three-dimensional video system based on integral photography,” Opt. Eng. 38, 1072–1077 (1997).
[CrossRef]

Other

J. Petersen, J. Lerner, “Homogenizer formed using coherent light and a holographic diffuser,” U.S. patent5,534,386 (9July1996).

M. Kobayashi, J. Arai, M. Okui, F. Okano, “Moire reducing method for integral photography display,” (Institute of Image Information and Television Engineers of Japan, 2002), Vol. 26, No. 74 (in Japanese).

M. Sawahata, S. Mikoshiba, S. Shirai, K. Oshita, “Tailring of an electron beam shape for reduction of CRT moire fringes,” in Proceedings of the 3rd International Display Workshops (Society of Information Display, 1996), Vol. 2, pp. 221–224.

J.-Y. Son, V. Saveljev, S.-H. Shin, Y.-J. Choi, S.-S. Kim, “Moire pattern reduction in full-parallax autostereoscopic imaging systems using two crossed lenticular plates as a viewing zone forming optics,” in Proceedings of the 10th International Display Workshops (Institute of Image Information and Television Engineers of Japan, and Society of Information Display, 2003), pp. 1401–1404.

M. Okui, M. Kobayashi, J. Arai, T. Mishina, F. Okano, “3-D display system,” Japanese patent application laid-open disclosure number JP 2004-118140 A (15April2004).

A. Schmidt, A. Grasnick, “Multiviewpoint autostereoscopic displays from 4D vision,” in Stereoscopic Displays and Virtual Reality Systems XI,A. J. Woods, J. O. Merritt, S. A. Benton, M. T. Bolas, eds., Proc. SPIE4660, 212–221 (2002).
[CrossRef]

L. Lipton, M. Feldman, “A new autostereoscopic display technology: the SynthaGram,” in Stereoscopic Displays and Virtual Reality Systems XI,A. J. Woods, J. O. Merritt, S. A. Benton, M. T. Bolas, eds., Proc. SPIE4660, 229–235 (2002).
[CrossRef]

K. Mashitani, G. Hamagishi, M. Higashino, T. Ando, S. Takemoto, “Step barrier system multiview glassless 3D display,” in Stereoscopic Displays and Virtual Reality Systems XI,A. J. Woods, J. O. Merritt, S. A. Benton, M. T. Bolas, eds., Proc. SPIE5291, 265–272 (2004).
[CrossRef]

M. McCormick, “Integral 3-D imaging for broadcast,” in Proceedings of the 2nd International Display Workshops, (Institute of Image Information and Television Engineers of Japan, 1995), Vol. 3, pp. 77–80.

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 (14)

Fig. 1
Fig. 1

Schematic of the basic principle of IP: (a) for pickup, numerous small elemental images are focused onto the film by a lens array, (b) for display, the light beams passing through the photograph retrace their original routes and converge at the point where the object was, forming an autostereoscopic image.

Fig. 2
Fig. 2

Color moire pattern caused by interference with the periodicity of the lens arrangement and the color filter structure.

Fig. 3
Fig. 3

Optical postfilter. Its use is necessary for reproduction of an original image when an image with a pixel structure is displayed.

Fig. 4
Fig. 4

Diffuser characteristics. The diffuser’s profile is assumed to be a Gaussian distribution with full width at half-maximum θ0. It is also assumed that the characteristics of the output beam are entirely dependent on the angle with the incident beam.

Fig. 5
Fig. 5

Diffuser as a spatial optical filter. The point light, which can be observed at x = 0 on the diffuser, is the summation of the light sources a and their neighboring area b. As a result, the image that appears on the diffuser’s surface can be regarded as an integral convolution of the displayed image and diffusing characteristics.

Fig. 6
Fig. 6

(a) Nondefocus condition, (b) defocus condition g < g0, (c) defocus condition g > g0. In (b) and (c) a circle area with radius RP is observed from viewing point V.

Fig. 7
Fig. 7

Luminance distribution model of a constant green signal on the display screen.

Fig. 8
Fig. 8

Experimental result of the diffusion effect: measured and calculated value of modulation. Relative modulation rM is given by rM = m/m0, where m and m0 are modulation factors with and without the diffuser, respectively.

Fig. 9
Fig. 9

Experimental result of the defocus effect: measured and calculated values of modulation. Relative modulation rM is given by rM = m/m0, where m and m0 are modulation factors with and without the diffuser, respectively.

Fig. 10
Fig. 10

Comparison of frequency characteristics of diffuser and defocus. Values Nα and Nβ are set at 1.137 and 1.205, respectively, to achieve attenuation as large as 40 dB at frequency ωs = 2π/Xs, where Xs is the pixel interval.

Fig. 11
Fig. 11

Distribution of energy ratio Rm, which indicates the strength of the moire. Rm is calculated as the ratio of Em, the energy of these components, to E0, the energy of the constant luminance.

Fig. 12
Fig. 12

Distribution of energy ratio Ed, the total energy of baseband components of the image. Expressing the necessary attenuation level of moire as shown in Fig. 11 yields efficient combinations of Nα and Nβ that give the maximum that can be found along the contour lines in this figure.

Fig. 13
Fig. 13

Comparison of Ed among diffuser, defocus, and combination by the proposed method. Calculation values when the required Rm is given are indicated.

Fig. 14
Fig. 14

Dependency of defocus filter on changes in the viewing distance. The required attenuation was designed at a viewing distance of 2 m.

Tables (1)

Tables Icon

Table 1 Equipment Specifications Used in the Experiment

Equations (18)

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

G ^ ( ω ) = P ( ω ) G D ( ω )
P ( ω ) = K 0 sin ( ω T S / 6 ) ω T S / 6 ,
G D ( ω ) = K 1 n = - G ( ω - n ω S ) .
S ( ω ) = K 2 m = - G ^ ( ω - m ω S ) = K 0 K 1 K 2 m = - { sin [ ( ω - m ω L ) T S / 6 ] ( ω - m ω L ) T S / 6 × n = - G ( ω - m ω L - n ω S ) } ,
H diff ( ω x ) = K 3 exp ( - ω x 2 X 0 2 4 a ) ,
X 0 θ 0 / d .
r p = r L ( 1 - g g 0 ) = r L [ g ( 1 L - 1 f ) - 1 ] ,
h Def ( r ) = { 1 r R p 0 r > R p ,
H Def ( ρ ) = 2 K 4 J 1 ( ρ R p ) ρ R p ,
H Def ( ω x ) = 2 K 4 J 1 ( ω x R p ) ω x R p .
q ( x ) = q 0 3 [ 1 + 2 n = 1 sin ( π n / 3 ) π n / 3 cos ( 2 π n x ) ] .
p ( x ) = q 0 3 [ H ( 0 ) + 2 n = 1 H ( 2 π n ) × sin ( π n / 3 ) π n / 3 cos ( 2 π n x ) ] ,
m = Max [ p ^ ( x ) ] - Min [ p ^ ( x ) ] Max [ p ^ ( x ) ] + Min [ p ^ ( x ) ] ,
H T ( ω ) = A ( ω ) H diff ( ω ) H Def ( ω ) = A ( ω ) K 3 exp ( - ω 2 X 0 2 4 a ) 2 K 4 J 1 ( ω x R p ) ω x R p ,
A ( ω ) = K 5 sin ( ω / 6 ) ( ω / 6 ) .
R m = E m / E 0 ,
E m = 2 n = 1 H T ( n ω s ) 2 ,             E 0 = H T ( 0 ) 2 ,
E d = 2 - ω s / 2 + ω s / 2 H T ( ω ) 2 d ω .

Metrics