Axial behavior of pupil-plane filters

Sheppard, Colin J. R.; Hegedűs, Zoltán

doi:10.1364/josaa.5.000643

Cited by 195 publications

(87 citation statements)

References 9 publications

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“…Such techniques can be attractive because they often provide a simple way to enhance the resolution of an optical system without resorting to more sophisticated near-field methods. An additional embodiment of optical super-resolution is the use of pupil-function engineering to manipulate the point spread function (PSF) at the focal plane of an imaging system, since the PSF has a radial profile whose shape depends sensitively on the aperture function of the system [91][92][93]. The PSF is defined as the irradiance distribution at the focal plane of an imaging system which is produced when imaging a point source [90].…”

Section: Conclusion and Future Developmentsmentioning

confidence: 99%

Solid immersion lens applications for nanophotonic devices

Ramsay¹

2008

J. Nanophoton

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Abstract. Solid immersion lens (SIL) microscopy combines the advantages of conventional microscopy with those of near-field techniques, and is being increasingly adopted across a diverse range of technologies and applications. A comprehensive overview of the state-of-the-art in this rapidly expanding subject is therefore increasingly relevant. Important benefits are enabled by SIL-focusing, including an improved lateral and axial spatial profiling resolution when a SIL is used in laser-scanning microscopy or excitation, and an improved collection efficiency when a SIL is used in a light-collection mode, for example in fluorescence micro-spectroscopy. These advantages arise from the increase in numerical aperture (NA) that is provided by a SIL. Other SIL-enhanced improvements, for example spherical-aberration-free sub-surface imaging, are a fundamental consequence of the aplanatic imaging condition that results from the spherical geometry of the SIL. The theory of SIL imaging exposes the unique properties of SILs that provide advantages in applications involving the interrogation of photonic and electronic nanostructures. Such applications range from the sub-surface examination of the complex three-dimensional microstructures fabricated in silicon integrated circuits, to quantum photoluminescence and transmission measurements in semiconductor quantum dot nanostructures.

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Section: Conclusion and Future Developmentsmentioning

confidence: 99%

Solid immersion lens applications for nanophotonic devices

Ramsay¹

2008

J. Nanophoton

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“…Sheppard and Hegedus [1] introduced transverse and axial gain factors describing the focusing properties of rotationally symmetric pupil filters or masks in the paraxial regime. These factors are expressed simply in terms of the moments of the pupil and avoid the necessity to calculate the diffracted field of the lens.…”

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Improved expressions for performance parameters for complex filters

et al. 2007

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Improved expressions are given for the performance parameters for transverse and axial gains for complex pupil filters. These expressions can be used to predict the behavior of filters that give a small axial shift in the focal intensity maximum and also predict the changes in gain for different observation planes. © 2007 Optical Society of America OCIS codes: 100.6640, 110.1220, 350.5730. Sheppard and Hegedus [1] introduced transverse and axial gain factors describing the focusing properties of rotationally symmetric pupil filters or masks in the paraxial regime. These factors are expressed simply in terms of the moments of the pupil and avoid the necessity to calculate the diffracted field of the lens. The treatment holds for real filters, which includes the class of amplitude filters, but also the important class of binary phase-only filters with a phase change of . De Juana et al.[2] extended the gain parameters to the case of general-phase filters, for the case when the intensity maximum is shifted only a small distance from the geometrical focus. Ledesma et al.[3] introduced an alternative approach for any complex filter, in which the plane of best focus is calculated first, and generalized gain parameters in the surroundings of the shifted focus are then calculated. This approach is much more flexible and is preferable for many phase filters, as the intensity peaks on the axis can be situated far from the geometrical focal plane, with the filter acting like a zone plate. But, unfortunately, it does not lead to analytic expressions for the filter parameters since numerical calculation of the plane of best focus is needed. Phase-only filters have advantages when the Strehl ratio is an important property (e.g., in astronomy), but for many applications when efficiency is not important the performance of amplitude filters is better, as the relative strength of the sidelobes is decreased [4,5]. The transverse and axial gains are calculated from the second derivatives of the transverse or axial intensity variations, normalized by the intensity. To obtain a second derivative to second order, and thus to get an expression for the gains as a function of axial position, an expression for intensity accurate to fourth order must be used. De Juana et al.'s [2] Eq. (8) for transverse gain is calculated from an expression containing a third-order term, while their Eq. (9) for axial gain is calculated from an expansion of intensity to only second order.In the paraxial Debye regime, the amplitude in the focal region of a lens is [6]where the optical coordinates for cylindrical coordinates r , z are v = ͑2r / ͒sin ␣, u = ͑8z / ͒sin 2 ͑␣ /2͒, with ␣ being the semiangle of convergence of the lens. We obtain for the intensity to fourth order in u for the case of a complex pupil:I͑v,u͒ = ͉I 0 ͉ 2 − u Im͑I 0

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“…4 -6 Continuously varying amplitude f ilters have also been investigated to produce transverse superresolution and (or) high DOF. 3,6,7 However, in recent years, phase-only filters have been studied to check whether they can improve the performance of amplitude-only f ilters. 1 In one approach, binary phase filters are used 1 to obtain elements that are easy to produce.…”

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Simple expressions for performance parameters of complex filters, with applications to super-Gaussian phase filters

et al. 2004

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To study the three-dimensional (3-D) behavior produced by complex filters, we have extended the expressions for the axial and the transverse gain to the case in which the best image plane is not near the paraxial focus. Super-Gaussian phase filters are proposed to control the 3-D image response of an optical system. Super-Gaussian phase filters depend on several parameters that modify the shape of the phase filter, producing tunable control of the 3-D response of the optical system. The filters are capable of producing a wide range of optical effects: transverse superresolution with high depth of focus, 3-D superresolution, and transverse apodization with different axial responses. © 2004 Optical Society of America OCIS codes: 110.0110, 220.0220, 350.5730, 220.1230. The three-dimensional (3-D) response of an optical system must be very different depending on its application. A common goal in many optical systems, for instance, in optical storage, 1 is to improve transverse resolution. Nevertheless, in most cases, a specific axial behavior is needed. For instance, in photolithography a high depth of focus (DOF) is also required. To achieve transverse superresolution, both in photolithography and in optical storage, very short wavelengths and high numerical apertures (NAs) are used. This has two effects: on one side the optical system must be well corrected (which is diff icult), and on the other high NA reduces the DOF (DOF is related to l͞NA 2 ). For this reason different superresolution techniques 2,3 have been proposed as ways to relax the optical system requirements or simply to improve the resolution of an optical system by providing enough DOF. In other systems, such as scanning microscopy, transverse and axial superresolution is desirable to obtain 3-D images. 4,5 There are different methods that have been used to modify the impulse response of an optical system. Annular transmission pupils have been widely used to improve transverse and (or) axial resolution. 4 -6 Continuously varying amplitude f ilters have also been investigated to produce transverse superresolution and (or) high DOF. 3,6,7 However, in recent years, phase-only filters have been studied to check whether they can improve the performance of amplitude-only f ilters. 1In one approach, binary phase filters are used 1 to obtain elements that are easy to produce. In other works continuous phase filters have been investigated, 8,9 but in some cases although transverse superresolution is obtained it is produced by very complex phase masks. 9In a recent study 8 a simple continuous phase filter was used to obtain transverse superresolution.In this Letter we propose super-Gaussian phase filters that have a shape that depends on four parameters. These parameters give us enough degrees of freedom to modify the whole 3-D image response in a controlled way. The f ilters are capable of producing a wide range of optical effects: they can produce transverse superresolution that increases the DOF, 3-D superresolution, and even transverse apodization ...

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Axial behavior of pupil-plane filters

Cited by 195 publications

References 9 publications

Solid immersion lens applications for nanophotonic devices

Solid immersion lens applications for nanophotonic devices

Improved expressions for performance parameters for complex filters

Simple expressions for performance parameters of complex filters, with applications to super-Gaussian phase filters

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