Abstract

Unobscured optical systems have been in production since the 1960s. In each case, the unobscured system is an intrinsically rotationally symmetric optical system with an offset aperture stop, a biased input field, or both. This paper presents a new family of truly nonsymmetric optical systems that exploit a new fabrication degree of freedom enabled by the introduction of slow-servos to diamond machining; surfaces whose departure from a sphere varies both radially and azimuthally in the aperture. The benefit of this surface representation is demonstrated by designing a compact, long wave infrared (LWIR) reflective imager using nodal aberration theory. The resulting optical system operates at F/1.9 with a thirty millimeter pupil and a ten degree diagonal full field of view representing an order of magnitude increase in both speed and field area coverage when compared to the same design form with only conic mirror surfaces.

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References

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  1. O. Cakmakci, B. Moore, H. Foroosh, and J. P. Rolland, “Optimal local shape description for rotationally non-symmetric optical surface design and analysis,” Opt. Express 16(3), 1583–1589 (2008).
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2010

2009

2008

2007

2005

1980

R. V. Shack and K. P. Thompson, “Influence of alignment errors of a telescope system,” Proc. SPIE 251, 146–153 (1980).

Cakmakci, O.

Foroosh, H.

Lundström, L.

Moore, B.

Nakano, T.

Rakich, A.

Rolland, J. P.

Schmid, T.

Shack, R. V.

R. V. Shack and K. P. Thompson, “Influence of alignment errors of a telescope system,” Proc. SPIE 251, 146–153 (1980).

Tamagawa, Y.

Thompson, K. P.

Unsbo, P.

Appl. Opt.

J. Opt. Soc. Am. A

Opt. Express

Proc. SPIE

R. V. Shack and K. P. Thompson, “Influence of alignment errors of a telescope system,” Proc. SPIE 251, 146–153 (1980).

Other

Synopsys Inc, “Zernike polynomials,” in CODE V Reference Manual, (2011), Volume IV, Appendix C.

Air Force Avionics Laboratory, “Three mirror objective,” in Aerial Camera Lenses, Report 027000 from RECON Central, the Reconnaissance Division/Reconnaissance Applications Branch, (1967), pp. 2–109.

J. M. Rodgers, “Catoptric optical system including concave and convex reflectors,” Optical Research Associates, US Patent 5,309,276 (1994).

J. W. Figoski, “Aberration characteristics of nonsymmetric systems,” in 1985 International Optical Design Conference, W.H. Taylor, and D.T. Moore, eds. (SPIE, 1985), pp. 104–111.

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Figures (9)

Fig. 1
Fig. 1

The sag components of a powered FRINGE Zernike polynomial surface (right, top) when the base conic surface (left, top) is superimposed with contributions of, top to bottom: spherical aberration (Z9), coma (Z7, Z8), and astigmatism (Z5, Z6). When the sag is evaluated with respect to the base conic (right, bottom), the Zernike overlay on the surface can be seen directly.

Fig. 2
Fig. 2

Demonstration of a beam footprint (grey dashed circle) from an off-axis field point striking a plane surface with 1λ Zernike spherical (Z9). It can be seen that the Zernike composition of the beam footprint sub-region contains components of Zernike coma and astigmatism by sequentially subtracting Zernike spherical and coma.

Fig. 3
Fig. 3

(a) Layout of U.S. Patent 5,309,276 consisting of three off-axis sections of rotationally symmetric mirrors and a fourth fold mirror (mirror 3). The optical system had, at the time of its design, the unique property of providing the largest planar, circular input aperture in the smallest overall spherical volume for a gimbaled application. (b) The new optical design based on tilted φ-polynomial surfaces to be coupled to an uncooled microbolometer.

Fig. 4
Fig. 4

(a) Layout for a fully obscured solution for a F/1.9, 10° full FOV LWIR imager. The system utilizes three conic mirror surfaces. (b) A Full Field Display (FFD) of the RMS wavefront error (RMS WFE) of the optical system. Each circle represents the magnitude of the RMS wavefront at a particular location in the field of view. The system exhibits a RMS WFE of < λ/250 over 10° full FOV.

Fig. 5
Fig. 5

The lens layout, Zernike coma (Z7, Z8) and astigmatism (Z5, Z6) full field displays for a ±40° FOV for the (a) on-axis optical system, (b) halfway tilted, 50% obscured system, and (c) fully tilted, 100% unobscured system. The region in red shows the field of interest, a 10° diagonal FOV.

Fig. 6
Fig. 6

The lower order spherical (Z9), coma (Z7, Z8), and astigmatism (Z5, Z6) and one higher order, elliptical coma (Z10, Z11) Zernike aberration contributions and RMS WFE FFDs over a ±5 degree field of view for the fully unobscured, on-axis solution. It can be seen that the system is dominated by field constant coma and astigmatism which are the largest contributors to the RMS WFE of ~12λ.

Fig. 7
Fig. 7

The lower order spherical (Z9), coma (Z7, Z8), and astigmatism (Z5, Z6) and one higher order, elliptical coma (Z10,11) Zernike aberration contributions and RMS WFE FFDs over a ±5 degree field of view for the optimized system where Zernike astigmatism and coma were used as variables on the secondary (stop) surface. When the system is optimized, the field constant contribution to astigmatism and coma are greatly reduced improving the RMS WFE from ~12λ to ~0.75λ.

Fig. 8
Fig. 8

The lower order spherical (Z9), coma (Z7, Z8), and astigmatism (Z5, Z6) and one higher order, elliptical coma (Z10, Z11) Zernike aberration contributions and RMS WFE FFDs over a ±5 degree field of view for the optimized system where Zernike coma is added as an additional variable to the tertiary surface. The RMS WFE has been reduced from ~0.75λ to ~0.25λ.

Fig. 9
Fig. 9

(a) Layout of LWIR imaging system optimized with φ-polynomial surfaces and (b) the RMS WFE of the final, optimized system, which is < λ/100 (0.01λ) at 10 µm over a 10° diagonal full FOV.

Equations (2)

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z=F( ρ,φ ),
z= c ρ 2 1+ 1( 1+k ) c 2 p 2 + j=1 16 C j Z j ,

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