Samir Mezouari

Phase pupil functions for reduction of defocus and spherical aberrations

Radially symmetric pupil plane phase retardation functions are derived that extend focal depth and alleviate third-order spherical aberration (SA) effects. The radial symmetry of these functions means that they can be more conveniently manufactured by use of traditional techniques such as diamond machining than previously reported filters with rectangular symmetry. The method employs minimization of the variation of Strehl ratio with defocus, W20, and SA, W40. The performance of the derived phase filters is illustrated by comparison with standard optical systems and with previously reported phase filters.

Circularly symmetric phase filters for control of primary third-order aberrations: coma and astigmatism

A quartic phase retardation function is described that reduces the variation of the intensity of the focal point of incoherent imaging systems suffering from primary third-order aberrations limited to coma and astigmatism. Corresponding modulation transfer functions are shown to remain practically invariant for moderate amounts of coma and astigmatism.

Amplitude and phase filters for mitigation of defocus and third-order aberrations

This paper gives a review on the design and use of both amplitude filters and phase filters to achieve a large focal depth in incoherent imaging systems. Traditional optical system design enhances the resolution of incoherent imaging systems by optical-only manipulations or some type of post-processing of an image that has been already recorded. A brief introduction to recent techniques to increase the depth of field by use of hybrid optical/digital imaging system is reported and its performance is compared with a conventional optical system. This technique, commonly named wavefront coding, employs an aspherical pupil plane element to encode the incident wavefront in such a way that the image recorded by the detector can be accurately restored over a large range of defocus. As reported in earlier work, this approach alleviates the effects of defocus and its related aberrations whilst maintaining diffraction-limited resolution. We explore the control of third order aberrations (spherical aberration, coma, astigmatism, and Petzval field curvature) through wavefront coding. This method offers the potential to implement diffraction-limited imaging systems using simple and low-cost lenses. Although these performances are associated with reductions in signal-to-noise ratio of the displayed image, the jointly optimized optical/digital hybrid imaging system can meet some specific requirements that are impossible to achieve with a traditional approach.

Validity of Fresnel and Fraunhofer approximations in scalar diffraction

Evaluation of the electromagnetic fields diffracted from plane apertures are, in the general case, highly problematic. Fortunately the exploitation of the Fresnel and more restricted Fraunhofer approximations can greatly simplify evaluation. In particular, the use of the fast Fourier transform algorithm when the Fraunhofer approximation is valid greatly increases the speed of computation. However, for specific applications it is often unclear which approximation is appropriate and the degree of accuracy that will be obtained. We build here on earlier work (Shimoji M 1995 Proc. 27th Southeastern Symp. on System Theory (Starkville, MS, March 1995) (Los Alamitos, CA: IEEE Computer Society Press) pp 520–4) that showed that for diffraction from a circular aperture and for a specific phase error, there is a specific curved boundary surface between the Fresnel and Fraunhofer regions. We derive the location of the boundary surface and the magnitude of the errors in field amplitude that can be expected as a result of applying the Fresnel and Fraunhofer approximations. These expressions are exact for a circular aperture and are extended to give the minimum limit on the domain of validity of the Fresnel approximation for plane arbitrary apertures.

Wavefront coding for aberration compensation in thermal imaging systems

As improving manufacturing techniques drive down the expense of imaging detector arrays, the total costs of future thermal imaging systems will become increasingly dominated by the manufacturing costs of the complex lens systems that are necessary for athermalization and achromatization. The concept of wavefront encoding combined with post-detection digital decoding has previously been shown to produce systems that are insensitive to thermal and chromatic defocus in slow imaging systems. In this paper we describe the application of the wavefront coding technique to thermal imaging systems with particular emphasis on the specific difficulties encountered. These difficulties include the use and effects of fast optics (~f/1), wide fields of view and noise amplification in low-contrast thermal images. Modeling results will be presented using diffraction models. We will describe the optimization of the wavefront encoding technique with a specific aim to reduce weight, size, and cost whilst maintaining acceptable imaging performance.

Combined amplitude and phase filters for increased tolerance to spherical aberration

Analysis of the expression for Strehl ratio for a circularly symmetric pupil allows one to design complex filters that offer reduced sensitivity to spherical aberration. It is shown that filters that combine hyper-Gaussian amplitude transmittance with hyper-Gaussian phase modulation provide five-fold reduction in sensitivity to spherical aberration. Furthermore, this is achieved without the introduction of zeros into the modulation transfer function and deconvolution can restore the transfer function to that of a diffraction-limited imager. The performance of the derived combined amplitude and phase filter is illustrated through the variation of its axial intensity versus spherical aberration. This technique is applicable to imaging in the presence of significant amounts of spherical aberration as is encountered in, for example, microscopy.

Primary aberrations alleviated with phase pupil filters

Conventional optical system design enhances the resolution of incoherent imaging systems by optical-only manipulations or some type of post-processing of an image that has been already formed. This paper gives a brief introduction to a modern method, which employs an aspherical phase filter to alter the transmitted wavefront in such a way that the optical system has a high tolerance to aberrations. As reported in earlier work, this approach alleviates the defocus and its related aberrations whilst maintaining the diffraction-limited resolution for incoherent imaging systems. We propose to explore the control of primary aberration through the use of radially symmetric phase filters and this include spherical aberration, coma, astigmatism, and Petzval field curvature aberration. This method offers the potential to implement diffraction-limited imaging systems using simple and low-cost one- or two-element lenses.

Wavefront-coded, Hybrid Imaging for the Alleviation of Optical Aberrations

Hybrid optical–digital imaging involves a combination of optical coding during image formation and digital decoding and image reconstruction. This process offers enhanced functionality beyond what is possible using conventional purely optical imaging, for example, in the fields of miniaturization, cost reduction, extended depth of field and three-dimentional imaging. This article focuses on one of the most important hybrid imaging techniques namely, wavefront coding, which was proposed principally as a means to extend the depth of field of an imaging system. A review of the theory behind wavefront coding, the manufacturing of wavefront-coding elements and various applications for which it has been proposed is provided.