Abstract

The color distortion arising around pattern edges of pictures scanned by a color image sensor using a GRIN rod lens is simulated by a model that uses a Gaussian distribution function as the spread function of the lens for two color separation systems. In the time division system, the maximum permissible ΔHB which indicates color aberration is obtained. Although this value depends on some sensor parameters, such as pixel size and pixel period, the method to obtain the maximum permissible ΔHB presented in this paper is suitable in almost all cases. In the space division system, the effect of color aberration on color distortion is clarified, and it is seen that permissible color aberration is larger than that in the time division systems.

© 1990 Optical Society of America

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References

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  1. K. Komiya, M. Kanzaki, T. Yamashita, “A 2048-Element Contact Type Image Sensor for Facsimile,” Technical Digest, International Electron Device Meeting (1981), pp. 309–312.
  2. S. Morozumi, H. Kurihara, T. Takeshita, H. Oka, K. Hasegawa, “Completely Integrated Contact-Type Linear Image Sensor,” IEEE Trans Electron Devices ED-32, 1546–1550 (1985).
    [CrossRef]
  3. N. Ohta, “Optimization of Spectral Sensitivities,” Photogr. Sci. Eng. 27, 193–201 (1983).
  4. Y. Hosaka, “High Precision Color Document Scanner,” in Proceedings, International Computer Color Graphics Conference (1983) pp. 120–139.
  5. H. Ohta, “Contact Type Color Image Sensor Using Switched Light Source,” in Proceedings, Sensoren-Technologie und Anwendung (NTG Fachberichte 93, Bad Nauheim, Germany (1986), pp. 21–26.

1985 (1)

S. Morozumi, H. Kurihara, T. Takeshita, H. Oka, K. Hasegawa, “Completely Integrated Contact-Type Linear Image Sensor,” IEEE Trans Electron Devices ED-32, 1546–1550 (1985).
[CrossRef]

1983 (1)

N. Ohta, “Optimization of Spectral Sensitivities,” Photogr. Sci. Eng. 27, 193–201 (1983).

Hasegawa, K.

S. Morozumi, H. Kurihara, T. Takeshita, H. Oka, K. Hasegawa, “Completely Integrated Contact-Type Linear Image Sensor,” IEEE Trans Electron Devices ED-32, 1546–1550 (1985).
[CrossRef]

Hosaka, Y.

Y. Hosaka, “High Precision Color Document Scanner,” in Proceedings, International Computer Color Graphics Conference (1983) pp. 120–139.

Kanzaki, M.

K. Komiya, M. Kanzaki, T. Yamashita, “A 2048-Element Contact Type Image Sensor for Facsimile,” Technical Digest, International Electron Device Meeting (1981), pp. 309–312.

Komiya, K.

K. Komiya, M. Kanzaki, T. Yamashita, “A 2048-Element Contact Type Image Sensor for Facsimile,” Technical Digest, International Electron Device Meeting (1981), pp. 309–312.

Kurihara, H.

S. Morozumi, H. Kurihara, T. Takeshita, H. Oka, K. Hasegawa, “Completely Integrated Contact-Type Linear Image Sensor,” IEEE Trans Electron Devices ED-32, 1546–1550 (1985).
[CrossRef]

Morozumi, S.

S. Morozumi, H. Kurihara, T. Takeshita, H. Oka, K. Hasegawa, “Completely Integrated Contact-Type Linear Image Sensor,” IEEE Trans Electron Devices ED-32, 1546–1550 (1985).
[CrossRef]

Ohta, H.

H. Ohta, “Contact Type Color Image Sensor Using Switched Light Source,” in Proceedings, Sensoren-Technologie und Anwendung (NTG Fachberichte 93, Bad Nauheim, Germany (1986), pp. 21–26.

Ohta, N.

N. Ohta, “Optimization of Spectral Sensitivities,” Photogr. Sci. Eng. 27, 193–201 (1983).

Oka, H.

S. Morozumi, H. Kurihara, T. Takeshita, H. Oka, K. Hasegawa, “Completely Integrated Contact-Type Linear Image Sensor,” IEEE Trans Electron Devices ED-32, 1546–1550 (1985).
[CrossRef]

Takeshita, T.

S. Morozumi, H. Kurihara, T. Takeshita, H. Oka, K. Hasegawa, “Completely Integrated Contact-Type Linear Image Sensor,” IEEE Trans Electron Devices ED-32, 1546–1550 (1985).
[CrossRef]

Yamashita, T.

K. Komiya, M. Kanzaki, T. Yamashita, “A 2048-Element Contact Type Image Sensor for Facsimile,” Technical Digest, International Electron Device Meeting (1981), pp. 309–312.

IEEE Trans Electron Devices (1)

S. Morozumi, H. Kurihara, T. Takeshita, H. Oka, K. Hasegawa, “Completely Integrated Contact-Type Linear Image Sensor,” IEEE Trans Electron Devices ED-32, 1546–1550 (1985).
[CrossRef]

Photogr. Sci. Eng. (1)

N. Ohta, “Optimization of Spectral Sensitivities,” Photogr. Sci. Eng. 27, 193–201 (1983).

Other (3)

Y. Hosaka, “High Precision Color Document Scanner,” in Proceedings, International Computer Color Graphics Conference (1983) pp. 120–139.

H. Ohta, “Contact Type Color Image Sensor Using Switched Light Source,” in Proceedings, Sensoren-Technologie und Anwendung (NTG Fachberichte 93, Bad Nauheim, Germany (1986), pp. 21–26.

K. Komiya, M. Kanzaki, T. Yamashita, “A 2048-Element Contact Type Image Sensor for Facsimile,” Technical Digest, International Electron Device Meeting (1981), pp. 309–312.

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Figures (10)

Fig. 1
Fig. 1

Color separation systems used with a GRIN rod lens: (a) space division system and (b) time division system.

Fig. 2
Fig. 2

Simulation model of color distortion at the pattern edges for a space division system: (a) document pattern; (b) reflective distribution of the document surface; (c) GRIN rod lens spread function; (d) light intensity distribution on the sensor surface; (e) signal level from each pixel.

Fig. 3
Fig. 3

Simulation model of color distortion at the pattern edges for time division systems: (a) light intensity distribution on the sensor surface; (b) signal level from each pixel (R-filter is above the sensor); (c) signal level from each pixel (G-filter is above the sensor); (d) signal level from each pixel (B-filter is above the sensor).

Fig. 4
Fig. 4

Output signals from a CCD linear sensor with a green filter placed on a document’s step pattern. The CCD pixel size was 14 μm.

Fig. 5
Fig. 5

Simulated output signals. The solid line shows simulation results; the circles show the measured output signals from Fig. 4.

Fig. 6
Fig. 6

Simulated color difference around the pattern edge in the image focused on the sensor surfaces and the reflective distribution of the document.

Fig. 7
Fig. 7

Simulation results on color differences from pattern edges for the output picture (time division system).

Fig. 8
Fig. 8

Color reproduction at the two peaks of ΔE*ab seen in Fig. 7. A and B are the points at the high side and low side peaks, respectively, and C is the point when there is no aberration.

Fig. 9
Fig. 9

Dependence on ΔHB of ΔE*ab at the high side and low side peaks.

Fig. 10
Fig. 10

ΔE*ab simulated on a space division system. Solid lines and dotted lines indicate the values ΔHB = 0 μm and ΔHB = 5 μm, respectively. (a), (b), and (c) are the cases when the pattern edge is above R, G, and B sensing pixels, respectively. The pixel size is 14 μm. The signal of one pixel in the output device is a combination of 3 pixel signals.

Tables (1)

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Table I Sensor Parameters Assumed In the Simulation

Equations (11)

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I ( x , λ ) = f ( x , λ ) exp [ - ( x - x ) 2 / H ( λ ) 2 ] d x ,
V i n = A n f ( x , λ ) exp [ - ( x - x ) 2 / H ( λ ) 2 ] S i d x d λ d x ,
V i n = C i A n f ( x ) exp [ - ( x - x ) 2 / H i 2 ] d x d x ,
H B = H G + Δ H B ,
H R = H G + Δ H R = H G + t Δ H B ,
t = [ T C ( λ R ) - T C ( λ G ) ] / [ T C ( λ G ) - T C ( λ B ) ] ,
C n = V R n r + V G n g + V B n b ,
Δ E * a b = [ ( Δ L * ) 2 + ( Δ a * ) 2 + ( Δ b * ) 2 ] 1 / 2 ,
L * = 116 ( Y / Y 0 ) 1 / 3 - 16 ,
a * = 500 [ ( X / X 0 ) 1 / 3 - ( Y / Y 0 ) 1 / 3 ] ,
b * = 200 [ ( X / X 0 ) 1 / 3 - ( Z / Z 0 ) 1 / 3 ] .

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