Abstract

We designed a cheap broadband uncooled microimager operating in the long-wavelength infrared range using only one lens at a minimal cost for the manufacturing process. The approach is based on thin optics where the device volume is small and therefore inexpensive materials can be used because some absorption can be tolerated. We have used a Fresnel lens on a thin silicon substrate. Up to now, Fresnel lenses have not been used for broadband imaging because of their chromatic properties. However, working in a relatively high diffraction order can significantly reduce chromatism. A prototype has been made for short range or indoor low-cost surveillance applications like people counting, and experimental images are presented.

© 2014 Optical Society of America

Uncooled infrared technologies are based on relatively inexpensive detectors and therefore offer an opportunity to open new types of markets, provided the whole system cost of imagers can be reduced as well. In recent years, important progress has been made in manufacturing low-cost uncooled long-wavelength infrared (LWIR) detectors that yet produce clear images [1]. To that end, sensor manufacturers have proposed to reduce the global size of the microbolometer array with a format around 80×80pixels [2]. Nevertheless, infrared optical elements are generally made with expensive materials like germanium and the challenge for the optical designer is to explore new designs using components made of cheap materials, such as silicon, chalcogenide glasses, or polyethylene. These components can be massively replicated either by photolithography or by molding process. Silicon and polyethylene are not commonly used in the LWIR spectral band because they are absorbing. Making of nearly flat Fresnel lenses on a thin substrate may, however, leave absorption to a tolerable level. If a camera based on a single thin component is designed, we expect to cut costs significantly.

As a reminder on diffractive Fresnel lenses [3], the principle is to conceptually cut a refractive lens into a set of annular slices of the same thickness, say e [see Fig. 1(a)]. If n(λ) is the refractive index at wavelength λ, then the component operates as a blazed diffractive lens in order m when (n(λ)1) e=m λ in the paraxial approximation. In many cases, Fresnel lenses are used in order 1 and are blazed for a given design wavelength λ0 at the “center” of the used spectal range, i.e., (n(λ0)1) e=λ0. But that is not always the case, see for example, [4] and [5]. In Fig. 1(b) is illustrated a Fresnel lens operating in the nominal order m0>1 at λ0. It is appropriate to comment that point here and explain why we use a higher-order Fresnel lens designed to work with m0 typically around 10 in the LWIR range.

 

Fig. 1. (a) First-order Fresnel lens. (b) m0th order Fresnel lens. Formulas are given in the paraxial approximation.

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As Fresnel lenses present a diffractive behavior, they exhibit a strong chromaticity. Specifically, if the design focal length at nominal wavelength λ0 is f0 and the nominal operating order at λ0 is m0, then the focal length f at wavelength λ in order m obeys

mλf=m0λ0f0,
i.e., there exists a considerable negative chromatic dispersion as the focal length is, in any given order, inversely proportional to the wavelength. That property has been used to compensate for chromatic aberration of refractive lenses in diffractive-refractive doublets typically operating in order 1 in the visible or in the infrared [6]. Indeed, because of the strong negative chromatic dispersion of diffractive lenses, while all glasses show positive index dispersion, a hybrid diffractive/refractive doublet can be made achromatic by associating a diffractive surface to an ordinary lens, with the diffractive structure possibly etched directly onto one of the lens surfaces. That mode of operation does not suit our needs because absorption by inexpensive materials for the LWIR domain precludes using a thick refractive lens. More complex designs are presented in [7] and [8] but they are not appropriate because they need to use several optical elements possibly made with different materials.

The idea, then, is to build upon the diffraction efficiency variation of Fresnel lenses versus wavelength. For a Fresnel lens operating in a given order m0 at wavelength λ0, the diffraction efficiency at wavelength λ in the order m is given by the following equation [9]:

ηm,λ=sinc2(mλ0(n(λ)1)λ(n(λ0)1)m0).

For a Fresnel lens operating in order 1, the diffraction efficiency smoothly decreases around the design wavelength, say around 10 μm, and would remain acceptable throughout the 7–14 μm spectral range but with an unacceptable factor 2 variation of the focal length [9]. However, for a higher-order Fresnel lens, the diffraction efficiency peak width around any blaze wavelength decreases in inverse proportion to order m. Indeed, neglecting refractive index dispersion for an order of magnitude calculation, for λ0=10μm and m0=12, the diffraction efficiency of order 12 drops to zero for λ=9.2μm and for λ=10.9μm. Nevertheless, at those two wavelengths, diffraction efficiency peaks at 100% in orders 13 and 11, respectively, and, according to Eq. (1), the corresponding focal length is just the design focal length f0. Therefore, although the focal length of each order suffers strong dispersion, the effective diffraction order shift with wavelength reduces the chromatic effects in Fresnel lenses operating at a relatively high order. Such a Fresnel lens may operate in the whole LWIR range with a focal length close to the design one, but the orders of interest will vary within the spectral range. However, this increases the required etching depth, which could become the limiting parameter even though improvements in fabrication methods have been achieved and a wide range of micro-optics can now be designed.

In this work, a specific compact and low-cost optical design based on a high-order Fresnel lens is introduced. To our knowledge, only a few earlier publications have introduced single diffractive lens systems for broadband and wide field of view imagery applications in the infrared domain. In [5], Sweeney used a system made of a single high-order Fresnel lens (m0=15) but his camera has a narrow field of view and is adapted for the visible spectrum. Moreover, image quality is degraded already at quite a small field angle.

The Zemax optical design software has been used to build a broadband infrared camera based on a landscape lens configuration. We will comment about that choice in the following paragraph. The lens that is used consists of a segmented aspherical profile etched on the flat surface facing the detector of a plane parallel plate. By this way, the whole optical power of the optical system is encoded in one single surface. The lens is a 1 mm thick high-order Fresnel lens made of silicon (m0=12 at λ0=10μm). The etching depth is equal to 50 μm and the lens is made of 10 useful diffractive zones. The system has an overall length of less than 3 mm with a focal length around 1 mm. It has a field of view around ±65° and an F-number of 1.5. It is illustrated in Fig. 2. The camera has been designed to operate in the LWIR region from 7 to 14 μm and it is compatible with a small uncooled 80×60pixels detector with 25 μm pixel-pitch.

 

Fig. 2. Setup of the built LWIR ultracompact landscape lens with a 12th order Fresnel lens in silicon. The three insets show the surface relief of the Fresnel lens on the illuminated area for three different field angles. (Red, θ=0°; blue, θ=30°; green, θ=65°).

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The landscape lens configuration is an interesting setup for a single-element wide-angle system. It is a very simple architecture that consists of one diaphragm followed by a converging singlet (which is here a high-order Fresnel lens) and the detector. It is of particular interest to minimize the field aberrations of a wide field of view camera [10]. The use of an aspheric underlying profile for the Fresnel lens was also helpful to further control aberrations. Additionally, the choice of a silicon substrate, with a very high index (3.5), was also interesting to limit aberrations. It is, however, important to note that the optimization has been done, for this first stage of the study, with the thin Fresnel lens Zemax surface type and pure geometrical optics quality assessments that only approximately model the true device behavior. Therefore, some discrepancies between approximated theoretical behavior and the measured experimental one could be anticipated, as will be effectively shown below.

A prototype of our camera has been assembled and is illustrated in Fig. 3. On the left is our Fresnel lens whose size is compared to a coin. On the right is the overall system (optics + detector + electronics) with its electronic module entirely controlled through USB interface, which could be miniaturized to meet industrial requirements. Our camera prototype works with an ULIS microbolometer composed of 160×120pixels with 25 μm pixel pitch, but the image fills only on a small part of the detector array, about 80×60pixels. The lens has been diamond turned by Savimex company.

 

Fig. 3. (a) Picture of the Fresnel lens. (b) Picture of the camera.

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Several measurements have been made to evaluate the optical performances of our camera. Indeed the noise equivalent temperature difference (NETD) of our system as well as its modulation transfer function (MTF) have been estimated. On the one hand, the NETD of our complete system, lens and detector, has been measured around 220 mK at f/1.5, which corresponds to about 100 mK at f/1. The evaluation of the NETD has been performed for 50×50pixels centered on the image (field of ±28°×±28°). Considering the fact that the illumination falloff over the field is quite low for our system (drop experimentally measured less than 25% from center to 42°), this “on-axis” value is expected to give an effective order of magnitude of the NETD on the whole useful field. On the other hand, the NETD of the detector alone has been measured to 75 mK at f/1. The degradation of the NETD obtained by adding the silicon lens in front of the detector can be explained by the 77% optical transmission coefficient of the (both sides antireflection coated) thin silicon plate in the 7–14 μm spectral range. We see that the global transmission decreases by only 23% when a 1 mm thick silicon plate is added in front of the detector. Thus, the use of a low-cost thin lens in silicon is shown to be an interesting choice for the design of a cheap uncooled LWIR camera. Indeed, the sensitivity of our camera would have been much more degraded using a silicon conventional thick lens.

Besides, the LWIR polychromatic MTF of our camera has been measured at different field angles by using the spot scan method. Our test bench is schematically drawn in Fig. 4. A blackbody illuminates a pinhole placed at the object focal plane of a collimator. The camera makes the image of that pinhole on the detector. We measure the signal delivered by the pixel whose intensity is maximum. It is our pixel of interest. Then we slightly move the camera in front of the collimator by subpixel shifts and for each position we measure the signal delivered by the pixel of interest. The displacement of the camera is made from rotational movements described by Euler angles. Thus, we obtain the well-sampled point spread function (PSF) of our imager. Then, according to [11] the MTF is given by the absolute value of the Fourier transform of the PSF (see Fig. 5). Our MTF measurements are compared with the MTF calculated from an infinitely thin Fresnel lens approximated model of the Zemax software. Zemax plots shown in Fig. 5 are taken on the full spectral band from about 2 to 14 μm with spectral weights estimated from an experimental transmission measurement of our camera. Thus, the material absorption, the atmospheric transmission, and the spectral response of the detector are fully considered. Theoretical MTF in Fig. 5 are obtained after extraction of Zemax data and taking into account the transfer function of the pixel.

 

Fig. 4. Test bench for MTF measurements.

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Fig. 5. System MTF for different field angles θ. (a) θ=0°, (b) θ=30°, (c) θ=50°. The maximum abscissa value corresponds to the Nyquist frequency of our detector.

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Figure 5 shows that experimental out of axis MTF curves stand significantly below the ones given by the approximated model from Zemax. That point could have been anticipated considering the fact that the Fresnel lens from Zemax is an ideal infinitely thin component. It does not take into account the true optical path of the light that goes through the real sawtooth-shaped component. We notice that the polychromatic PSF essentially extends in the radial direction when the field angle increases, which leads to a significant drop of the tangential MTF, as shown in Fig. 5. We are currently theoretically investigating this peculiar behavior with more accurate diffractive modeling of the real shape Fresnel lens in order to understand and try to circumvent the problem in future designs. However, for a camera that is dedicated to short-range surveillance applications, the design is mainly driven by the cost, and some tradeoff on the image quality can be considered.

Some images have been recorded with our microcamera. The picture in Fig. 6 has been taken in a room and is dedicated to surveillance applications, such as people detection and counting. The image is shown after nonuniformity correction, bad pixels identification and replacement, and distortion correction. In this picture, people can be detected and some details of the scene can be seen.

 

Fig. 6. Picture taken with our camera.

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To conclude, a low-cost infrared microcamera has been designed, manufactured, and characterized. The prototype consists only of a diaphragm, a high-order Fresnel lens on a thin silicon plate, and a detector. The overall thickness of the optical system is below 3 mm. The imager has a full field of view of 130° and an F-number of 1.5. It is optimized in the spectral band from about 7 to 14 μm. Our camera is shown to be well-suited for low-cost surveillance applications where priority is given to the reduction of the cost even though the image quality is slightly reduced. Presently, the used Fresnel lens is in silicon and has been made by direct diamond turning. Direct diamond turning is very effective in generating continuous diffractive profile, so it was a good candidate to make first experimental performance measurements. However, as this manufacturing process is expensive and time consuming [12], it is not ideal for the mass production of optical components. In future works, we will think about replication manufacturing techniques. In particular we will consider the method that consists of etching a silicon wafer to produce a high number of lenses by photolithography [1315]. Another idea will be to explore the potentials of molding processes. A mold would be manufactured and then large number of lenses could be massively replicated [16,17]. In this option, our design will have to be adapted to inexpensive materials that can be molded, such as chalcogenide or polyethylene.

This work was sponsored by the French Procurement Agency (DGA) of the Ministry of Defense.

References

1. A. Rogalski, Infrared Phys. Technol. 43, 187 (2002). [CrossRef]  

2. P. Robert, F. Trolez, E. Bercier, H. Clerambault, A. Touvignon, and J. L. Tissot, in Proceedings of the IRSf2 2013 (2013), p. 24 .

3. K. Miyamoto, J. Opt. Soc. Am. 51, 17 (1961). [CrossRef]  

4. D. Falkis and G. M. Morris, Appl. Opt. 34, 2462 (1995). [CrossRef]  

5. D. W. Sweeney and G. E. Sommargen, Appl. Opt. 34, 2469 (1995). [CrossRef]  

6. G. P. Behrmann and J. N. Mait, in Micro-Optics: Elements, Systems and Applications (CRC Press, 1997), Chap. 10, pp. 259–292.

7. Z. Liping, L. Y. Loy, Z. Yan, and Y. Zhisheng, Proc. SPIE 3897, 624 (1999). [CrossRef]  

8. A. P. Wood and P. J. Rogers, Proc. SPIE 5865, 58650B (2005). [CrossRef]  

9. G. J. Swanson, “Binary optics technology: the theory and design of multi-level diffractive optical elements,” Technical Report 854, Massachusetts Institute of Technology, Lincoln Laboratory (1989).

10. D. A. Buralli and G. M. Morris, Appl. Opt. 28, 3950 (1989). [CrossRef]  

11. J. W. Goodman, in Introduction to Fourier Optics, 3rd ed. (Roberts & Company, 2005), Chap. 6, pp. 138–145.

12. R. Gläbe and O. Riemer, Proc. SPIE 7716, 771602 (2010). [CrossRef]  

13. D. C. O’Shea, T. J. Suleski, A. D. Kathman, and D. W. Prather, in Diffractive Optics: Design, Fabrication, and Test (SPIE, 2004), Chap. 7, pp. 133–147.

14. T. Takahata, K. Matsumoto, and I. Shimoyama, in The 17th International Conference on Solid-State Sensors, Actuators and Microsystems (2013), p. 1408.

15. J. Choi, A. A. Cruz-Cabrera, and A. Tanbakuchi, Proc. SPIE 8612, 86120G (2013). [CrossRef]  

16. G. Cogburn, A. Symmons, and L. Mertus, Proc. SPIE 7660, 766020 (2010). [CrossRef]  

17. A. Symmons and R. Pini, Proc. SPIE 8704, 870425 (2013). [CrossRef]  

References

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  1. A. Rogalski, Infrared Phys. Technol. 43, 187 (2002).
    [CrossRef]
  2. P. Robert, F. Trolez, E. Bercier, H. Clerambault, A. Touvignon, and J. L. Tissot, in Proceedings of the IRSf2 2013 (2013), p. 24 .
  3. K. Miyamoto, J. Opt. Soc. Am. 51, 17 (1961).
    [CrossRef]
  4. D. Falkis and G. M. Morris, Appl. Opt. 34, 2462 (1995).
    [CrossRef]
  5. D. W. Sweeney and G. E. Sommargen, Appl. Opt. 34, 2469 (1995).
    [CrossRef]
  6. G. P. Behrmann and J. N. Mait, in Micro-Optics: Elements, Systems and Applications (CRC Press, 1997), Chap. 10, pp. 259–292.
  7. Z. Liping, L. Y. Loy, Z. Yan, and Y. Zhisheng, Proc. SPIE 3897, 624 (1999).
    [CrossRef]
  8. A. P. Wood and P. J. Rogers, Proc. SPIE 5865, 58650B (2005).
    [CrossRef]
  9. G. J. Swanson, “Binary optics technology: the theory and design of multi-level diffractive optical elements,” , Massachusetts Institute of Technology, Lincoln Laboratory (1989).
  10. D. A. Buralli and G. M. Morris, Appl. Opt. 28, 3950 (1989).
    [CrossRef]
  11. J. W. Goodman, in Introduction to Fourier Optics, 3rd ed. (Roberts & Company, 2005), Chap. 6, pp. 138–145.
  12. R. Gläbe and O. Riemer, Proc. SPIE 7716, 771602 (2010).
    [CrossRef]
  13. D. C. O’Shea, T. J. Suleski, A. D. Kathman, and D. W. Prather, in Diffractive Optics: Design, Fabrication, and Test (SPIE, 2004), Chap. 7, pp. 133–147.
  14. T. Takahata, K. Matsumoto, and I. Shimoyama, in The 17th International Conference on Solid-State Sensors, Actuators and Microsystems (2013), p. 1408.
  15. J. Choi, A. A. Cruz-Cabrera, and A. Tanbakuchi, Proc. SPIE 8612, 86120G (2013).
    [CrossRef]
  16. G. Cogburn, A. Symmons, and L. Mertus, Proc. SPIE 7660, 766020 (2010).
    [CrossRef]
  17. A. Symmons and R. Pini, Proc. SPIE 8704, 870425 (2013).
    [CrossRef]

2013 (2)

J. Choi, A. A. Cruz-Cabrera, and A. Tanbakuchi, Proc. SPIE 8612, 86120G (2013).
[CrossRef]

A. Symmons and R. Pini, Proc. SPIE 8704, 870425 (2013).
[CrossRef]

2010 (2)

G. Cogburn, A. Symmons, and L. Mertus, Proc. SPIE 7660, 766020 (2010).
[CrossRef]

R. Gläbe and O. Riemer, Proc. SPIE 7716, 771602 (2010).
[CrossRef]

2005 (1)

A. P. Wood and P. J. Rogers, Proc. SPIE 5865, 58650B (2005).
[CrossRef]

2002 (1)

A. Rogalski, Infrared Phys. Technol. 43, 187 (2002).
[CrossRef]

1999 (1)

Z. Liping, L. Y. Loy, Z. Yan, and Y. Zhisheng, Proc. SPIE 3897, 624 (1999).
[CrossRef]

1995 (2)

1989 (1)

1961 (1)

Behrmann, G. P.

G. P. Behrmann and J. N. Mait, in Micro-Optics: Elements, Systems and Applications (CRC Press, 1997), Chap. 10, pp. 259–292.

Bercier, E.

P. Robert, F. Trolez, E. Bercier, H. Clerambault, A. Touvignon, and J. L. Tissot, in Proceedings of the IRSf2 2013 (2013), p. 24 .

Buralli, D. A.

Choi, J.

J. Choi, A. A. Cruz-Cabrera, and A. Tanbakuchi, Proc. SPIE 8612, 86120G (2013).
[CrossRef]

Clerambault, H.

P. Robert, F. Trolez, E. Bercier, H. Clerambault, A. Touvignon, and J. L. Tissot, in Proceedings of the IRSf2 2013 (2013), p. 24 .

Cogburn, G.

G. Cogburn, A. Symmons, and L. Mertus, Proc. SPIE 7660, 766020 (2010).
[CrossRef]

Cruz-Cabrera, A. A.

J. Choi, A. A. Cruz-Cabrera, and A. Tanbakuchi, Proc. SPIE 8612, 86120G (2013).
[CrossRef]

Falkis, D.

Gläbe, R.

R. Gläbe and O. Riemer, Proc. SPIE 7716, 771602 (2010).
[CrossRef]

Goodman, J. W.

J. W. Goodman, in Introduction to Fourier Optics, 3rd ed. (Roberts & Company, 2005), Chap. 6, pp. 138–145.

Kathman, A. D.

D. C. O’Shea, T. J. Suleski, A. D. Kathman, and D. W. Prather, in Diffractive Optics: Design, Fabrication, and Test (SPIE, 2004), Chap. 7, pp. 133–147.

Liping, Z.

Z. Liping, L. Y. Loy, Z. Yan, and Y. Zhisheng, Proc. SPIE 3897, 624 (1999).
[CrossRef]

Loy, L. Y.

Z. Liping, L. Y. Loy, Z. Yan, and Y. Zhisheng, Proc. SPIE 3897, 624 (1999).
[CrossRef]

Mait, J. N.

G. P. Behrmann and J. N. Mait, in Micro-Optics: Elements, Systems and Applications (CRC Press, 1997), Chap. 10, pp. 259–292.

Matsumoto, K.

T. Takahata, K. Matsumoto, and I. Shimoyama, in The 17th International Conference on Solid-State Sensors, Actuators and Microsystems (2013), p. 1408.

Mertus, L.

G. Cogburn, A. Symmons, and L. Mertus, Proc. SPIE 7660, 766020 (2010).
[CrossRef]

Miyamoto, K.

Morris, G. M.

O’Shea, D. C.

D. C. O’Shea, T. J. Suleski, A. D. Kathman, and D. W. Prather, in Diffractive Optics: Design, Fabrication, and Test (SPIE, 2004), Chap. 7, pp. 133–147.

Pini, R.

A. Symmons and R. Pini, Proc. SPIE 8704, 870425 (2013).
[CrossRef]

Prather, D. W.

D. C. O’Shea, T. J. Suleski, A. D. Kathman, and D. W. Prather, in Diffractive Optics: Design, Fabrication, and Test (SPIE, 2004), Chap. 7, pp. 133–147.

Riemer, O.

R. Gläbe and O. Riemer, Proc. SPIE 7716, 771602 (2010).
[CrossRef]

Robert, P.

P. Robert, F. Trolez, E. Bercier, H. Clerambault, A. Touvignon, and J. L. Tissot, in Proceedings of the IRSf2 2013 (2013), p. 24 .

Rogalski, A.

A. Rogalski, Infrared Phys. Technol. 43, 187 (2002).
[CrossRef]

Rogers, P. J.

A. P. Wood and P. J. Rogers, Proc. SPIE 5865, 58650B (2005).
[CrossRef]

Shimoyama, I.

T. Takahata, K. Matsumoto, and I. Shimoyama, in The 17th International Conference on Solid-State Sensors, Actuators and Microsystems (2013), p. 1408.

Sommargen, G. E.

Suleski, T. J.

D. C. O’Shea, T. J. Suleski, A. D. Kathman, and D. W. Prather, in Diffractive Optics: Design, Fabrication, and Test (SPIE, 2004), Chap. 7, pp. 133–147.

Swanson, G. J.

G. J. Swanson, “Binary optics technology: the theory and design of multi-level diffractive optical elements,” , Massachusetts Institute of Technology, Lincoln Laboratory (1989).

Sweeney, D. W.

Symmons, A.

A. Symmons and R. Pini, Proc. SPIE 8704, 870425 (2013).
[CrossRef]

G. Cogburn, A. Symmons, and L. Mertus, Proc. SPIE 7660, 766020 (2010).
[CrossRef]

Takahata, T.

T. Takahata, K. Matsumoto, and I. Shimoyama, in The 17th International Conference on Solid-State Sensors, Actuators and Microsystems (2013), p. 1408.

Tanbakuchi, A.

J. Choi, A. A. Cruz-Cabrera, and A. Tanbakuchi, Proc. SPIE 8612, 86120G (2013).
[CrossRef]

Tissot, J. L.

P. Robert, F. Trolez, E. Bercier, H. Clerambault, A. Touvignon, and J. L. Tissot, in Proceedings of the IRSf2 2013 (2013), p. 24 .

Touvignon, A.

P. Robert, F. Trolez, E. Bercier, H. Clerambault, A. Touvignon, and J. L. Tissot, in Proceedings of the IRSf2 2013 (2013), p. 24 .

Trolez, F.

P. Robert, F. Trolez, E. Bercier, H. Clerambault, A. Touvignon, and J. L. Tissot, in Proceedings of the IRSf2 2013 (2013), p. 24 .

Wood, A. P.

A. P. Wood and P. J. Rogers, Proc. SPIE 5865, 58650B (2005).
[CrossRef]

Yan, Z.

Z. Liping, L. Y. Loy, Z. Yan, and Y. Zhisheng, Proc. SPIE 3897, 624 (1999).
[CrossRef]

Zhisheng, Y.

Z. Liping, L. Y. Loy, Z. Yan, and Y. Zhisheng, Proc. SPIE 3897, 624 (1999).
[CrossRef]

Appl. Opt. (3)

Infrared Phys. Technol. (1)

A. Rogalski, Infrared Phys. Technol. 43, 187 (2002).
[CrossRef]

J. Opt. Soc. Am. (1)

Proc. SPIE (6)

J. Choi, A. A. Cruz-Cabrera, and A. Tanbakuchi, Proc. SPIE 8612, 86120G (2013).
[CrossRef]

G. Cogburn, A. Symmons, and L. Mertus, Proc. SPIE 7660, 766020 (2010).
[CrossRef]

A. Symmons and R. Pini, Proc. SPIE 8704, 870425 (2013).
[CrossRef]

R. Gläbe and O. Riemer, Proc. SPIE 7716, 771602 (2010).
[CrossRef]

Z. Liping, L. Y. Loy, Z. Yan, and Y. Zhisheng, Proc. SPIE 3897, 624 (1999).
[CrossRef]

A. P. Wood and P. J. Rogers, Proc. SPIE 5865, 58650B (2005).
[CrossRef]

Other (6)

G. J. Swanson, “Binary optics technology: the theory and design of multi-level diffractive optical elements,” , Massachusetts Institute of Technology, Lincoln Laboratory (1989).

J. W. Goodman, in Introduction to Fourier Optics, 3rd ed. (Roberts & Company, 2005), Chap. 6, pp. 138–145.

D. C. O’Shea, T. J. Suleski, A. D. Kathman, and D. W. Prather, in Diffractive Optics: Design, Fabrication, and Test (SPIE, 2004), Chap. 7, pp. 133–147.

T. Takahata, K. Matsumoto, and I. Shimoyama, in The 17th International Conference on Solid-State Sensors, Actuators and Microsystems (2013), p. 1408.

P. Robert, F. Trolez, E. Bercier, H. Clerambault, A. Touvignon, and J. L. Tissot, in Proceedings of the IRSf2 2013 (2013), p. 24 .

G. P. Behrmann and J. N. Mait, in Micro-Optics: Elements, Systems and Applications (CRC Press, 1997), Chap. 10, pp. 259–292.

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Figures (6)

Fig. 1.
Fig. 1.

(a) First-order Fresnel lens. (b)  m 0 th order Fresnel lens. Formulas are given in the paraxial approximation.

Fig. 2.
Fig. 2.

Setup of the built LWIR ultracompact landscape lens with a 12th order Fresnel lens in silicon. The three insets show the surface relief of the Fresnel lens on the illuminated area for three different field angles. (Red, θ = 0 ° ; blue, θ = 30 ° ; green, θ = 65 ° ).

Fig. 3.
Fig. 3.

(a) Picture of the Fresnel lens. (b) Picture of the camera.

Fig. 4.
Fig. 4.

Test bench for MTF measurements.

Fig. 5.
Fig. 5.

System MTF for different field angles θ . (a)  θ = 0 ° , (b)  θ = 30 ° , (c)  θ = 50 ° . The maximum abscissa value corresponds to the Nyquist frequency of our detector.

Fig. 6.
Fig. 6.

Picture taken with our camera.

Equations (2)

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m λ f = m 0 λ 0 f 0 ,
η m , λ = sinc 2 ( m λ 0 ( n ( λ ) 1 ) λ ( n ( λ 0 ) 1 ) m 0 ) .

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