Infrared imaging with a wavefront-coded singlet lens Gonzalo Muyo1, Amritpal Singh2, Mathias Andersson2, David Huckridge3, Andrew Wood4 and Andrew R. Harvey1,* 1
School of Engineering and Physical Sciences, Heriot-Watt University, Edinburgh, EH14 4AS, United Kingdom 2 Development and Technology Sensors, SAAB Bofors Dynamics AB, Göteborg, SE-402 51, Sweden 3 Qinetiq, Malvern, WR14 3PS, United Kingdom 4 Qioptiq, St Asaph, LL17 0LL, United Kingdom *
[email protected]
Abstract: We describe the use of wavefront coding for the mitigation of optical aberrations in a thermal imaging system. Diffraction-limited imaging is demonstrated with a simple singlet which enables an approximate halving in length and mass of the optical system compared to an equivalent twoelement lens. 2009 Optical Society of America OCIS codes: (110.1758) Computational imaging; (110.3080) Infrared imaging; (110.4850) Optical transfer functions; (110.7348) Wavefront encoding.
References and links 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19.
J. Mait, R. Athale, and J. van der Gracht, "Evolutionary paths in imaging and recent trends," Opt. Express 11, 2093-2101 (2003). E. Dowski and T. W. Cathey, “Extended depth of field through wavefront coding,” Appl. Opt. 34, 18591866 (1995). K. Kubala, E. R. Dowski, and W. T. Cathey, “Reducing complexity in computational imaging systems,” Opt. Express 11, 2102-2108 (2003). G. Muyo and A. R. Harvey, “Wavefront coding for athermalization of infrared imaging systems,” Proc. SPIE Vol. 5612, p. 227-235 (2004). M. Demenikov, E. Findlay, and A. R. Harvey, “Miniaturization of zoom lenses with a single moving element,” Opt. Express 17, 6118-6127 (2009). G. Muyo and A. R. Harvey, “The effect of detector sampling in wavefront-coded imaging systems,” J. Opt. A: Pure Appl. Opt. 11, 054002 (2009). G. Muyo and A. R. Harvey, “Decomposition of the optical transfer function: wavefront coding imaging systems,” Opt. Lett. 30, 2715-2717 (2005). D. Zalvidea and E. E. Sicre, “Phase Pupil Functions for Focal-Depth Enhancement Derived from a Wigner Distribution Function,” Appl. Opt. 37, 3623-3627 (1998). W. Chi and N. George, “Electronic imaging using a logarithmic asphere,” Opt. Lett. 26, 875-877 (2001). S. Mezouari and A. R. Harvey, “Phase pupil functions for reduction of defocus and spherical aberrations,” Opt. Lett. 28, 771-773 (2003). S. Mezouari, G. Muyo, and A. R. Harvey, “Circularly symmetric phase filters for control of primary thirdorder aberrations: coma and astigmatism,” J. Opt. Soc. Am. A 23, 1058-1062 (2006). S. Prasad, T. C. Torgersen, V. P. Pauca, R. J. Plemmons, and J. van der Gracht, “Engineering the pupil phase to improve image quality,” Proc. SPIE Vol. 5108, 1-12 (2003). S. S. Sherif, W. T. Cathey, and E. R. Dowski, “Phase Plate to Extend the Depth of Field of Incoherent Hybrid Imaging Systems,” Appl. Opt. 43, 2709-2721 (2004). A. Sauceda and J. Ojeda-Castañeda, “High focal depth with fractional-power wave fronts,” Opt. Lett. 29, 560-562 (2004). G. Muyo, A. R. Harvey, and A. Singh, “High-performance thermal imaging with a singlet and pupil plane encoding,” Proc. SPIE 5987, 162-169 (2005). G. Muyo; A. Singh, M. Andersson, D. Huckridge, and A. Harvey, “Optimized thermal imaging with a singlet and pupil plane encoding: experimental realization,” Proc. SPIE 6395, U211-U219 (2006). G. D.B oreman, Modulation transfer function in optical and electro-optical systems (SPIE Press, Bellingham, WA, 2001). T. Vettenburg, A. Wood, N. Bustin, and A. R. Harvey, “Optimality of pupil-phase profiles for increasing the defocus tolerance of hybrid digital-optical imaging systems,” Proc SPIE 7429, 742903 (2009). doi: 10.1117/12.825119. W. C. Karl, “Regularization in image restoration and reconstruction,” in Handbook of Image and Video Processing, A. Bovik, ed., (Academic Press 2000).
#117589 - $15.00 USD
(C) 2009 OSA
Received 22 Sep 2009; revised 26 Oct 2009; accepted 1 Nov 2009; published 5 Nov 2009
9 November 2009 / Vol. 17, No. 23 / OPTICS EXPRESS 21118
20. D. S. C. Biggs and M. Andrews, “Acceleration of iterative image restoration algorithms,” Appl. Opt. 36, 1766-1775 (1997).
1. Introduction As the cost of uncooled thermal imaging detectors decreases year-on-year in accordance with Moore’s law, the total cost of infrared systems is increasingly dominated by the manufacturing costs of the lenses [1]. With conventional optical design, multi-element aspheric lenses are required to provide wide-field, near-diffraction-limited imaging with the fast optics required for good radiometric sensitivity. We report here the design and manufacture of a thermal imaging lens that uses wavefront coding [2] to mitigate off-axis aberrations and enable a field-of-view (FoV) that is approximately double that of a conventional singlet lens and functionality comparable to a more complex compound lens. In recent years, wavefront coding has been shown to significantly increase tolerance to manufacturing inaccuracies and various aberrations, in particular those related to defocus such as thermal and chromatic defocus, field curvature and astigmatism [2-5]. Wavefront coding involves a spatial phase-modulation at the exit pupil so as to produce a specific point-spread function (PSF) and a distinctively blurred, or one might say, encoded image. The important characteristics are that the modulation-transfer-function (MTF) then exhibits no nulls for the design frequency range; nominally those frequencies falling below the Nyquist frequency of the detector array [6], and the PSF is approximately invariant with respect to an increased range of variations in optical aberrations. The absence of nulls in the MTF [7] enables a highfidelity image to be recovered by digital inversion whilst the invariance of the PSF simplifies inversion by enabling a single kernel to be used. The phase function may be rotationally symmetric [8-11] or anti-symmetric [2, 12-14], however antisymmetry offers, in general, a better trade of aberration mitigation against reduction in signal-to-noise ratio (SNR). The performance enhancement of a wavefront-coded imaging system is subject to some limitations: the signal-to-noise ratio in the recovered image is necessarily lower than in the recorded image; accurate manufacture of an antisymmetric phase-function with a peak-tovalley height of just a few microns is difficult to achieve using conventional manufacturing techniques; and less widely reported, modest variations in the PSF introduce image artefacts. These are important factors in the trade-off design of a wavefront-coded imaging system. We have previously reported the possibility of using wavefront coding to enable elimination of the Petzval field-flattening element from a two-element infrared lens to yield a singlet with software image recovery for correction of aberrations [15, 16]. Without wavefront coding, the performance of the optimised singlet lens was limited by high levels of off-axis aberrations. We showed that introduction of an antisymmetric phase-function into the front surface of the singlet combined with digital image-recovery, would enable high-quality imaging across an extended field-of-view. We report here the optimisation and manufacture of this imaging system and results from improved image restoration algorithms. To provide flexibility for this demonstration, the phase-function was implemented as a discrete phasemask as a prelude to future incorporation of the phase-function into the front surface of the singlet. The singlet lens and phase-plate are both machined from germanium and used with a long-wave, thermal infrared (8-12µm) uncooled focal plane array (FPA). In the next section we describe the design, manufacture and assessment of the singlet imaging system; image recovery and experimental results are described in section three and in section four we present conclusions. 2. Development of a wavefront-coded thermal infrared singlet 2.1 Conventional thermal IR imaging system: from two lenses to singlet We appraise here the merit of wavefront coding for simplification and size-reduction of an exemplar high-performance fast-lens, as shown in Fig. 1(a). The original F/1, 75mm focallength lens employed a meniscus front element with an aspherical back surface, to minimise coma and spherical aberration. A Petzval rear element was included to reduce field curvature #117589 - $15.00 USD
(C) 2009 OSA
Received 22 Sep 2009; revised 26 Oct 2009; accepted 1 Nov 2009; published 5 Nov 2009
9 November 2009 / Vol. 17, No. 23 / OPTICS EXPRESS 21119
and astigmatism and yield virtually diffraction-limited performance across a field-of-view (FoV) of 9×7 degrees. When integrated with an uncooled, long-wave infrared FPA of 320×240 pixels on a 38µm pitch (micro-bolometer from FLIR Systems) optical aberrations are insignificant. A singlet lens of equivalent f-number and focal length, as shown in Fig. 1(b), is obtained by removal of the Petzval element followed by re-optimisation of both surfaces of the front element to minimise aberrations although high levels of field curvature and astigmatism are unavoidable: up to 10 waves at the primary wavelength of 10µm. It is noteworthy that the removal of the Petzval element has enabled a 45% reduction in the optical track; from 142mm to 78mm and a similar fractional reduction in mass. The variation of the MTF with FoV is illustrated in Fig. 2(a) for this singlet for frequencies up to the Nyquist frequency of the detector. Note the significant disparity between the sagittal and tangential MTFs arising from the astigmatic wavefronts and the presence of nulls in the MTF with increasing FoV, which result in irrecoverable loss of information. The pixelated PSFs [17] shown in Fig. 2(b), illustrate the large spatial variation that results in the blurring of the detected image. The re-optimized singlet was manufactured by single-point diamond machining. An example image of the World Trade Centre area in Stockholm acquired with the singlet is displayed in Fig. 3(a). As expected, the image is sharp only in the central area and is significantly degraded towards the edges of the image.
(a)
(b)
Fig. 1. (a). Original germanium IR lens and (b). re-optimised aspheric singlet
(a)
(b)
Fig. 2. (a). Singlet polychromatic tangential and sagittal MTFs for various field angles up to the Nyquist frequency and (b) corresponding pixelated PSFs at field angles of 0, 2.5 and 3.5° degrees in horizontal and vertical directions. MTF plots incorporate the pixel MTF [17].
#117589 - $15.00 USD
(C) 2009 OSA
Received 22 Sep 2009; revised 26 Oct 2009; accepted 1 Nov 2009; published 5 Nov 2009
9 November 2009 / Vol. 17, No. 23 / OPTICS EXPRESS 21120
(a)
(b)
Fig. 3. (a) Image from the singlet only of the World Trade Centre area in Stockholm. (b) image recorded with singlet and phase mask prior to digital decoding.
Optimal implementation of wavefront coding involves a trade of noise amplification against FoV: mitigation of higher off-axis aberrations requires increased amplitude of phase modulation and the resultant MTF suppression causes higher levels of noise amplification during image recovery. For optimal image quality, we have chosen to mitigate aberrations only within a FoV of 7º, which involves up to six waves of aberration. 2.2 Design and fabrication of the germanium phase mask Antisymmetric phase-functions of the general form [12]
θ (x, y ) = α (x 3 + y 3 ) + β (x 2 y + xy 2 ), where |x|
