Abstract

We analyze an optical system after inserting a simple quartic phase plate in its pupil plane to extend the focal depth. The system is used specifically to track distant objects like stars. We design an optimum quartic phase plate for a real lens system which has an effective focal length of 29 mm, an F-number of 1.6, a field of view of 20 degrees, and a working wavelength range of 0.5~0.75 µm. By introducing the quartic phase plate, we enhance the focal depth of the system more than threefold as compared to a system having no phase plate.

© 2003 Optical Society of America

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References

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  1. Carl Christian Liebe, �??Accuracy performance of star tracking-a tutorial,�?? IEEE Transactions on Aerospace and Electronic Systems 38, 587-599 (April 2002).
    [CrossRef]
  2. G. Borghi, D. Procopio, M. Magnani, et al., �??Stellar reference unit for CASSINI mission,�?? Proc. SPIE 2210, 150-161 (1994).
    [CrossRef]
  3. Giancarlo Rufino and Domenico Accardo, �??Enhancement of the centroiding algorithm for star tracker measure refinement,�?? Acta Astronautica, 53, 135-147 (2003).
    [CrossRef]
  4. Carl Christian Liebe, �??Star trackers for attitude determination,�?? IEEE AES Systems Magazines, 10-16 (June 1995).
    [CrossRef]
  5. Kazuhide Noguchi, Koshi Sato, et al., �??CCD star tracker for attitude determination and control of satellite for space VLBI mission,�?? Proc. SPIE 2810, 190-200 (1996).
    [CrossRef]
  6. Joseph F. Kordas, Isabella T. Lewis, et al., �??Star tracker stellar compass for the Clementine mission,�?? Proc. SPIE 2466, 70-83 (1995).
    [CrossRef]
  7. Dobryna Zalvidea and Enrique E. Sicre, �??Phase pupil functions for focal-depth enhancement derived from -a Wigner distribution function,�?? Appl. Opt. 37, 3623-3627 (1998).
    [CrossRef]

Acta Astronautica (1)

Giancarlo Rufino and Domenico Accardo, �??Enhancement of the centroiding algorithm for star tracker measure refinement,�?? Acta Astronautica, 53, 135-147 (2003).
[CrossRef]

Appl. Opt. (1)

IEEE AES Systems Magazines (1)

Carl Christian Liebe, �??Star trackers for attitude determination,�?? IEEE AES Systems Magazines, 10-16 (June 1995).
[CrossRef]

IEEE Transactions on Aerospace and Elect (1)

Carl Christian Liebe, �??Accuracy performance of star tracking-a tutorial,�?? IEEE Transactions on Aerospace and Electronic Systems 38, 587-599 (April 2002).
[CrossRef]

Proc. SPIE (3)

G. Borghi, D. Procopio, M. Magnani, et al., �??Stellar reference unit for CASSINI mission,�?? Proc. SPIE 2210, 150-161 (1994).
[CrossRef]

Kazuhide Noguchi, Koshi Sato, et al., �??CCD star tracker for attitude determination and control of satellite for space VLBI mission,�?? Proc. SPIE 2810, 190-200 (1996).
[CrossRef]

Joseph F. Kordas, Isabella T. Lewis, et al., �??Star tracker stellar compass for the Clementine mission,�?? Proc. SPIE 2466, 70-83 (1995).
[CrossRef]

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Figures (6)

Fig. 1.
Fig. 1.

On-axis intensity for different values of z.

Fig. 2.
Fig. 2.

Fraction of enclosed energy for a diameter of 30 µm and different values of α.

Fig. 3.
Fig. 3.

Configuration of an optical system comprising no phase plate.

Fig. 4.
Fig. 4.

Spot size containing 80% energy in an optical system comprising no quartic phase plate for different defocus values.

Fig. 5.
Fig. 5.

OPD curves of an optical system with a quartic phase plate.

Fig. 6.
Fig. 6.

Spot size containing 80% energy in an of the optical system comprising a quartic phase plate for different values of axis distance

Equations (9)

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d 0 = 2.44 λ F .
z = DF ,
ϕ ( ρ ) = π · α · ( ρ 4 ρ 0 4 ρ 2 ρ 0 2 ) ,
I ( r , z ) = 2 π 0 ρ 0 J 0 ( 2 π λ 0 · r f 0 · ρ ) exp [ i · π · α · ( ρ 4 ρ 0 4 ρ 2 ρ 0 2 ) ] exp ( i π λ 0 · f 0 2 · z · ρ 2 ) ρ d ρ 2 .
I ( 0 , z ) = 2 π 0 ρ 0 exp [ i · π · α · ( ρ 4 ρ 0 4 ρ 2 ρ 0 2 ) ] exp ( i π λ 0 · f 0 2 · z · ρ 2 ) ρ d ρ 2 .
RED ( c ) = 0 c 2 π · I ( r ) · r · d r 0 2 π · I ( r ) · r · d r .
ϕ ( ρ ) = ± π · 28 · ( ρ 4 ρ 0 4 ρ 2 ρ 0 2 ) .
ϕ ( ρ ) = π · 22.3 · [ ( ρ 4 ρ 0 4 ) ( ρ 2 ρ 0 2 ) ] .
ϕ ( ρ ) = π · [ α 1 · ( ρ 4 ρ 0 4 ) α 2 · ( ρ 2 ρ 0 2 ) ] .

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