Abstract

The modulation transfer function (MTF) is the main parameter that is used to evaluate image quality in electro-optical systems. Detector sampling MTF in most electro-optical systems determines the cutoff frequency of the system. The MTF of the detector depends on its pixel shape. In this work, we calculated the MTF of a detector with an equilateral triangular pixel shape. Some new results were found in deriving the MTF for the equilateral triangular pixel shape.

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References

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  1. M. Shannon, The Art and Science of Optical Design (Cambridge University, 2000).
  2. M. Gu, Advanced Optical Imaging Theory (Springer, 2000).
  3. G. C. Holst, CCD Arrays, Cameras, and Displays (SPIE, 1998).
  4. B.-T. Tan, X. Guan, and X. H. Guo, “Study on imaging simulation of telescope for space target,” in International Conference on Electronics and Optoelectronics (ICEOE, 2011), pp. V3-185–V3-188.
  5. O. Yadid-Pecht, “The geometrical modulation transfer function (MTF) for different pixel active area shapes,” Opt. Eng. 39, 859–865 (2000).
    [CrossRef]
  6. K. J. Barnard and G. D. Boreman, “Modulation transfer function of hexagonal staring focal plane arrays,” Opt. Eng. 30, 1915–1919 (1991).
    [CrossRef]

2000 (1)

O. Yadid-Pecht, “The geometrical modulation transfer function (MTF) for different pixel active area shapes,” Opt. Eng. 39, 859–865 (2000).
[CrossRef]

1991 (1)

K. J. Barnard and G. D. Boreman, “Modulation transfer function of hexagonal staring focal plane arrays,” Opt. Eng. 30, 1915–1919 (1991).
[CrossRef]

Barnard, K. J.

K. J. Barnard and G. D. Boreman, “Modulation transfer function of hexagonal staring focal plane arrays,” Opt. Eng. 30, 1915–1919 (1991).
[CrossRef]

Boreman, G. D.

K. J. Barnard and G. D. Boreman, “Modulation transfer function of hexagonal staring focal plane arrays,” Opt. Eng. 30, 1915–1919 (1991).
[CrossRef]

Gu, M.

M. Gu, Advanced Optical Imaging Theory (Springer, 2000).

Guan, X.

B.-T. Tan, X. Guan, and X. H. Guo, “Study on imaging simulation of telescope for space target,” in International Conference on Electronics and Optoelectronics (ICEOE, 2011), pp. V3-185–V3-188.

Guo, X. H.

B.-T. Tan, X. Guan, and X. H. Guo, “Study on imaging simulation of telescope for space target,” in International Conference on Electronics and Optoelectronics (ICEOE, 2011), pp. V3-185–V3-188.

Holst, G. C.

G. C. Holst, CCD Arrays, Cameras, and Displays (SPIE, 1998).

Shannon, M.

M. Shannon, The Art and Science of Optical Design (Cambridge University, 2000).

Tan, B.-T.

B.-T. Tan, X. Guan, and X. H. Guo, “Study on imaging simulation of telescope for space target,” in International Conference on Electronics and Optoelectronics (ICEOE, 2011), pp. V3-185–V3-188.

Yadid-Pecht, O.

O. Yadid-Pecht, “The geometrical modulation transfer function (MTF) for different pixel active area shapes,” Opt. Eng. 39, 859–865 (2000).
[CrossRef]

Opt. Eng. (2)

O. Yadid-Pecht, “The geometrical modulation transfer function (MTF) for different pixel active area shapes,” Opt. Eng. 39, 859–865 (2000).
[CrossRef]

K. J. Barnard and G. D. Boreman, “Modulation transfer function of hexagonal staring focal plane arrays,” Opt. Eng. 30, 1915–1919 (1991).
[CrossRef]

Other (4)

M. Shannon, The Art and Science of Optical Design (Cambridge University, 2000).

M. Gu, Advanced Optical Imaging Theory (Springer, 2000).

G. C. Holst, CCD Arrays, Cameras, and Displays (SPIE, 1998).

B.-T. Tan, X. Guan, and X. H. Guo, “Study on imaging simulation of telescope for space target,” in International Conference on Electronics and Optoelectronics (ICEOE, 2011), pp. V3-185–V3-188.

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Figures (5)

Fig. 1.
Fig. 1.

Equilateral triangular pixel array detector. U and D show the apex up and apex down triangles, respectively.

Fig. 2.
Fig. 2.

Geometry of the apex up and apex down triangle pixel shapes.

Fig. 3.
Fig. 3.

Two-dimensional graphical representation of the triangular pixel MTF.

Fig. 4.
Fig. 4.

Contour plot of the triangular pixel MTF.

Fig. 5.
Fig. 5.

Contour plot of the rectangular pixel MTF.

Equations (18)

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s(x,y)={1As(x,y)S0(x,y)S,
PSFdetector=s(x,y).
OTFdetector=F{s(x,y)},
MTFdetector=|F{s(x,y)}|.
PSFpixel=triang(x,y).
OTFup(u,v)=4a23(0a32(a2y33)(a2y33)e2πiudx)e2πivdy=1π2a23u[eπiue2πiy(uv/3)v+u/3eπiue2πiy(u+v/3)vu/3]y=0y=a32=2[cos(πav3)cos(πau)]3π2a2(v2u23)+2i[sin(πav3)+vu3sin(πau)]3π2a2(v2u23).
OTFup(u,v)=4a23(0a32(a2y33)(a2y33)e2πiudx)e2πivdy=1π2a23u[eπiue2πiy(uv/3)v+u/3eπiue2πiy(u+v/3)vu/3]y=0y=a32=2[cos(πav3)cos(πau)]3π2a2(v2u23)+2i[sin(πav3)+vu3sin(πau)]3π2a2(v2u23).
|OTFup|=|OTFdown|,
MTFtrianglepixel=MTFup=MTFdown.
MTFtrianglepixel(u,v)=2[cos(πav3)cos(πau)]2+[vu3sin(πau)sin(πav3)]23π2a2(v2u23).
MTFtrianglepixel(u,v)=2[cos(πpv3)cos(πpu)]2+[vu3sin(πpu)sin(πpv3)]23π2a2(v2u23).
d1:u=0,d2:v=u3,d3:v=u3.
MTFtrianglepixel(u,v=±u3)=2pπa2u[sin(πpu)]2+[cos(πpu)sin(πpu)πpu]2.
MTFtrianglepixel(u=0,v)=2p[cos(πpv3)1]2+[sin(πpv3)+πpv3]2a2(πpv3)2.
MTFrectangular(u,v)=|sin(πau)πausin(πbv)πbv|.
l1:u=1a,l2:u=1a,l3:v=1b,l4:v=1b.
[cos(πav3)cos(πau)]2+[vu3sin(πau)sin(πav3)]2=0.
cos(πav3)=cos(πau),sin(πav3)=sin(πau)=0u=k1ak1Z;v=k1+2k2a3k2Z.

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