Abstract

This paper explores lens design through thermal analysis and correction of 4-megapixel DLP projector lenses at temperatures ranging from 10°C to 80°C, and analyzes and discusses the TV distortion and lateral color with a focal length of 24 mm, F/# of 1.71, projection distance of 7.2 m, and projection screen size of 200 inches. Appropriate lens materials are selected and changes are made to the lens barrel materials to achieve athermalization. At temperatures from 10°C to 80°C, the image quality of lens is as follows: MTF (93 lp/mm) is greater than 0.554, lateral color is less than 1.39 µm, optical distortion is less than 0.147%, TV distortion is less than 0.079%, and relative illumination less than 92.52%.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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    [Crossref]
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2012 (1)

Y. Bai, T. W. Xing, W. M. Lin, and W. M. Xie, “Athermalization of middle infrared optical system,” J. Appl. Opt. 33(1), 181–185 (2012).

1997 (1)

1994 (1)

1991 (2)

J. L. Rayces and L. Lebich, “Thermal compensation of infrared achromatic objectives with three optical materials,” Proc. SPIE 1354, 752–759 (1991).
[Crossref]

P. J. Rogers, “Athermalized FLIR optics,” Proc. SPIE 1354, 742–751 (1991).
[Crossref]

1989 (1)

M. Roberts and P. J. Rogers, “Wide waveband infrared optics,” Proc. SPIE 1013, 84–91 (1989).
[Crossref]

1986 (1)

1984 (1)

T. H. Jamieson, “Ultrawide waveband optics,” Opt. Eng. 23(2), 111–116 (1984).
[Crossref]

1976 (1)

1948 (1)

Bai, Y.

Y. Bai, T. W. Xing, W. M. Lin, and W. M. Xie, “Athermalization of middle infrared optical system,” J. Appl. Opt. 33(1), 181–185 (2012).

Duggin, M. J.

Grey, D. S.

Hashimoto, T.

Horman, M. H.

Jamieson, T. H.

T. H. Jamieson, “Ultrawide waveband optics,” Opt. Eng. 23(2), 111–116 (1984).
[Crossref]

Lebich, L.

J. L. Rayces and L. Lebich, “Thermal compensation of infrared achromatic objectives with three optical materials,” Proc. SPIE 1354, 752–759 (1991).
[Crossref]

Lin, W. M.

Y. Bai, T. W. Xing, W. M. Lin, and W. M. Xie, “Athermalization of middle infrared optical system,” J. Appl. Opt. 33(1), 181–185 (2012).

Rayces, J. L.

J. L. Rayces and L. Lebich, “Thermal compensation of infrared achromatic objectives with three optical materials,” Proc. SPIE 1354, 752–759 (1991).
[Crossref]

Roberts, M.

M. Roberts and P. J. Rogers, “Wide waveband infrared optics,” Proc. SPIE 1013, 84–91 (1989).
[Crossref]

Rogers, P. J.

P. J. Rogers, “Athermalized FLIR optics,” Proc. SPIE 1354, 742–751 (1991).
[Crossref]

M. Roberts and P. J. Rogers, “Wide waveband infrared optics,” Proc. SPIE 1013, 84–91 (1989).
[Crossref]

Tajime, T.

Tamagawa, Y.

Wakabayashi, S.

Xie, W. M.

Y. Bai, T. W. Xing, W. M. Lin, and W. M. Xie, “Athermalization of middle infrared optical system,” J. Appl. Opt. 33(1), 181–185 (2012).

Xing, T. W.

Y. Bai, T. W. Xing, W. M. Lin, and W. M. Xie, “Athermalization of middle infrared optical system,” J. Appl. Opt. 33(1), 181–185 (2012).

Appl. Opt. (4)

J. Appl. Opt. (1)

Y. Bai, T. W. Xing, W. M. Lin, and W. M. Xie, “Athermalization of middle infrared optical system,” J. Appl. Opt. 33(1), 181–185 (2012).

J. Opt. Soc. Am. (1)

Opt. Eng. (1)

T. H. Jamieson, “Ultrawide waveband optics,” Opt. Eng. 23(2), 111–116 (1984).
[Crossref]

Proc. SPIE (3)

M. Roberts and P. J. Rogers, “Wide waveband infrared optics,” Proc. SPIE 1013, 84–91 (1989).
[Crossref]

J. L. Rayces and L. Lebich, “Thermal compensation of infrared achromatic objectives with three optical materials,” Proc. SPIE 1354, 752–759 (1991).
[Crossref]

P. J. Rogers, “Athermalized FLIR optics,” Proc. SPIE 1354, 742–751 (1991).
[Crossref]

Other (3)

Schott, “TIE-29: Refractive index and dispersion,” in Proc. Schott Technical information (Schott Inc., Germany, 2015).

Schott, “TIE-19: Temperature coefficient of the refractive index,” in Proc. Schott Technical information (Schott Inc., Germany, July 2008).

TEXAS INSTRUMENT, “DLP 660TE 0.66 4 K UHD DMD,” http://www.ti.com/lit/ds/symlink/dlp660te.pdf

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Figures (15)

Fig. 1.
Fig. 1. Schematic diagram of horizontal distortion
Fig. 2.
Fig. 2. Schematic diagram of vertical distortion
Fig. 3.
Fig. 3. Image circle of projection lens
Fig. 4.
Fig. 4. Horizontal line warping in screen image
Fig. 5.
Fig. 5. The angles between the ideal image height in the horizontal direction and vertical height
Fig. 6.
Fig. 6. Warping in the horizontal direction
Fig. 7.
Fig. 7. Vertical line warping in the screen image
Fig. 8.
Fig. 8. The angles between the ideal image height in the vertical direction and horizontal height
Fig. 9.
Fig. 9. Warping in the vertical direction
Fig. 10.
Fig. 10. Locations of the DMD, human eye and screen in the projection system
Fig. 11.
Fig. 11. Relationship between horizontal TV distortion and horizontal warping
Fig. 12.
Fig. 12. Definition of angles θa and θb in the horizontal direction
Fig. 13.
Fig. 13. Relationship between vertical TV distortion and vertical warping
Fig. 14.
Fig. 14. Schematic diagram of lateral color
Fig. 15.
Fig. 15. Drawing of projection lens

Tables (7)

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Table 1. Temperature changes of lens parameters and the thermal expansion coefficient

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Table 2. TI DLP 660TE 0.66′′ specifications

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Table 3. Design specifications of projection lens

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Table 4. Parameters related to athermalization of the lens

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Table 5. Data for the projection lens

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Table 6. Aspherical coefficient data for the projection lens

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Table 7. Lens image quality at temperature from 10°C to 80°C

Equations (24)

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n 2 ( λ ) 1 = B 1 λ 2 ( λ 2 C 1 ) + B 2 λ 2 ( λ 2 C 2 ) + B 3 λ 2 ( λ 2 C 3 ) ,
d n ( λ , T ) d T = n 2 ( λ , T 0 ) 1 2 n ( λ , T 0 ) × ( D 0 + 2 D 1 Δ T + 3 D 2 Δ T 2 + E 0 + 2 E 1 Δ T λ 2 λ T K 2 ) ,
n ( λ , T ) = n ( λ , T 0 ) + d n ( λ , T ) d T Δ T ,
z = C r 2 1 + 1 ( 1 + K ) C 2 r 2 + a 4 r 4 + a 6 r 6 + a 8 r 8 + . ,
d ϕ d T = ϕ ( 1 n 1 d n d T α ) = γ ϕ ,
γ = 1 n 1 d n d T α .
Total power : i = 1 j ϕ i = ϕ ,
Athermalization : i = 1 j d ϕ i d T + β ϕ = 0 ,
y offset = ( C B ) × 100 % ,
h = A 2 + ( B + C ) 2 .
optical distortion = real image height ideal image height ideal image height × 100 % .
T V D H = Δ 1 h V p 100 % .
T V D V = Δ 2 h H p 100 % .
Δ 1 = | h M A X h M I N | .
Δ 2 =   | h m a x   h m i n | .
Θ || = 60   tan 1 ( Δ 1 L ) ,
Θ = 60   t a n 1 ( Δ 2 L ) ,
h a = h a R cos θ a = h a R × h 0.75 p h a p .
h b = h b R cos θ b = h b R × h 0.75 p h b p .
Δ 1 = | h a h b | = | h a R × h 0.75 p h a p h b R × h 0.75 p h b p | .
T V D H = Δ 1 h 0.75 p 100 % = | h a R h a p h b R h b p | × 100 % = | h a R h a p h a p × 100 % h b R h b p h b p × 100 % | = | O D a O D b | .
Δ 2 = | h a h b | .
T V D V = Δ 2 h 0.66 p 100 % = | O D a O D b | .
Θ λ = 60   tan 1 Δ λ L .