Dmitry Reshidko

Optical analysis of miniature lenses with curved imaging surfaces

Miniature cameras for consumer electronics and mobile phones have been, and continue to be, in fast development. The system level requirements, such as manufacturing cost, packaging, and sensor characteristics, impose unique challenges for optical designers. In this paper, we discuss the potential optical benefits of having a curved image surface rather than a flat one. We show that curved sensor technology allows for optically faster lens solutions. We discuss trade-offs of several relevant characteristics, such as packaging, chief ray angle, image quality, and tolerance sensitivity. A comparison of a benchmark flat field lens, and an evaluation design imaging on a curved surface and working at f/1.6, provides useful specific insights. For a given image quality, departing from a flat imaging surface does not allow significantly reducing the total length of a lens.

Role of aberrations in the relative illumination of a lens system

Several factors impact the light irradiance and relative illumination produced by a lens system at its image plane. In addition to cosine-fourth-power radiometric law, image and pupil aberrations and light vignetting also count. We use an irradiance transport equation to derive a closed form solution that provides insight into how individual aberration terms affect the light irradiance and relative illumination. The theoretical results are in agreement with real ray tracing.

Method for the design of nonaxially symmetric optical systems using free-form surfaces

Abstract. A systematic method for the design of nonaxially symmetric optical systems is described. Free-form optical surfaces are constructed by superposition of a conic segment and a polynomial, and successfully applied to design relatively fast wide field-of-view optical systems.

Aspheric/freeform optical surface description for controlling illumination from point-like light sources

We present an optical surface in closed form that can be used to design lenses for controlling relative illumination on a target surface. The optical surface is constructed by rotation of the pedal curve to the ellipse about its minor axis. Three renditions of the surface are provided, namely as an expansion of a base surface, and as combinations of several base surfaces. Examples of the performance of the surfaces are presented for the case of a point light source.

A method for the design of unsymmetrical optical systems using freeform surfaces

Optical systems that do not have axial symmetry can provide useful and unique solutions to certain imaging problems. However, the complexity of the optical design task grows as the degrees of symmetry are reduced and lost: there are more aberration terms to control, and achieving a sharp image over a wide field-of-view at fast optical speeds becomes challenging. Plane-symmetric optical systems represent a large family of practical non-axially symmetric systems that are simple enough to be easily described and thus are well understood. Design methodologies and aberration theory of plane-symmetric optical systems have been discussed in the literature, and various interesting solutions have been reported [1-4]. The little discussed in the literature technique of confocal systems is effective for the design of unsymmetrical optics. A confocal unsymmetrical system is constructed in such a way that there is sharp image along a given ray (called the optical axis ray (OAR)) surface after surface. It is possible to show that such a system can have a reduced number of field aberrations, and that the system will behave closer to an axially symmetric system [5-6]. In this paper, we review a methodology for the design of unsymmetrical optical systems. We utilize an aspherical/freeform surface constructed by superposition of a conic expressed in a coordinate system that is centered on the off-axis surface segment rather than centered on the axis of symmetry, and an XY polynomial. The conic part of the aspherical/freeform surface describes the base shape that is required to achieve stigmatic imaging surface after surface along the OAR. The XY polynomial adds a more refined shape description to the surface sag and provides effective degrees of freedom for higher-order aberration correction. This aspheric/freeform surface profile is able to best model the ideal reflective surface and to allow one to intelligently approach the optical design. Examples of two- and threemirror unobscured wide field-of-view reflective systems are provided to show how the methods and corresponding aspheric/freeform surface are applied. We also demonstrate how the method can be extended to design a monolithic freeform objective.

The role of aberrations in the relative illumination of a lens system

Several factors impact the light irradiance and relative illumination produced by a lens system at its image plane. In addition to the cosine-fourth-power radiometric law, image and pupil aberrations, and light vignetting also count. In this paper, we use an irradiance transport equation to derive a closed form solution that provides insight into how individual aberration terms affect the light irradiance and relative illumination. The theoretical results are in agreement with real ray tracing.

Ray Tracing Methods for Correcting Chromatic Aberrations in Imaging Systems

The correction of chromatic aberrations is typically performed using aberration formulas or by using real ray tracing. While the use of aberration formulas might be effective for some simple optical systems, it has limitations for complex and fast systems. For this reason chromatic aberration correction is usually accomplished with real ray tracing. However, existing optimization tools in lens design software typically mix the correction of monochromatic and chromatic aberrations by construction of an error function that minimizes both aberrations at the same time. This mixing makes the correction of one aberration type dependent on the correction of the other aberration type. We show two methods to separate the chromatic aberrations correction of a lens system. In the first method we use forward and reverse ray tracing and fictitious nondispersive glasses, to cancel the monochromatic aberration content and allow the ray tracing optimization to focus mainly on the color correction. On the second method we provide the algorithm for an error function that separates aberrations. Furthermore, we also demonstrate how these ray tracing methods can be applied to athermalize an optical system. We are unaware that these simple but effective methods have been already discussed in detail by other authors.

Geometrical irradiance changes in a symmetric optical system

Abstract. The concept of the aberration function is extended to define two functions that describe the light irradiance distribution at the exit pupil plane and at the image plane of an axially symmetric optical system. Similar to the wavefront aberration function, the irradiance function is expanded as a polynomial, where individual terms represent basic irradiance distribution patterns. Conservation of flux in optical imaging systems is used to derive the specific relation between the irradiance coefficients and wavefront aberration coefficients. It is shown that the coefficients of the irradiance functions can be expressed in terms of wavefront aberration coefficients and first-order system quantities. The theoretical results—these are irradiance coefficient formulas—are in agreement with real ray tracing.

Optical design study and prototyping of a dual-field zoom lens imaging in the 1-5 micron infrared waveband

Optical systems can provide simultaneous imaging in several spectral bands and thus be much more useful. A new and current generation of focal plane arrays is allowing detection in more than one spectral region. The design of a refractive imaging lens for such detectors requires correcting chromatic aberrations over the wider range of wavelengths. However, the fewer available refracting materials, the material properties that change between the spectral bands, and the system transmission requirements make the design of such lenses particularly challenging. We present a dual-field zoom lens designed for a cooled detector sensing across short-wave infrared (SWIR) and midwave infrared (MWIR) spectral bands (continuous imaging for 1-5 μm). This zoom lens has a 75 mm focal length in the wide mode and a 250mm focal length in the narrow mode, and operates at f/4.7 in both discrete zoom positions. The lens is actively compensated to work in thermal environments from -20°C to +60°C. We discuss the optical design methodology, review the selection of materials and coatings for the optical elements, and analyze the transmission of the lens and optical performance. A prototype system has been manufactured and assembled. We validate our design with experimental data.

Algorithms and examples for chromatic aberration correction and athermalization of complex imaging systems

Ray tracing methods for correcting chromatic aberration of imaging system are described. Monochromatic and chromatic aberration correction is separated into two independent problems. A similar method is applied to athermalize an optical system.