Analytic design method for optimal imaging: coupling three ray sets using two free-form lens profiles

In this work, a new two-dimensional optics design method is proposed that enables the coupling of three ray sets with two lens surfaces. The method is especially important for optical systems designed for wide field of view and with clearly separated optical surfaces. Fermat’s principle is used to deduce a set of functional differential equations fully describing the entire optical system. The presented general analytic solution makes it possible to calculate the lens profiles. Ray tracing results for calculated 15th order Taylor polynomials describing the lens profiles demonstrate excellent imaging performance and the versatility of this new analytic design method.

Perfect imaging of three object points with only two analytic lens surfaces in two dimensions

In this work, a new two-dimensional analytic optics design method is presented that enables the coupling of three ray sets with two lens profiles. This method is particularly promising for optical systems designed for wide field of view and with clearly separated optical surfaces. However, this coupling can only be achieved if different ray sets will use different portions of the second lens profile. Based on a very basic example of a single thick lens, the Simultaneous Multiple Surfaces design method in two dimensions (SMS2D) will help to provide a better understanding of the practical implications on the design process by an increased lens thickness and a wider field of view. Fermat?s principle is used to deduce a set of functional differential equations fully describing the entire optical system. The transformation of these functional differential equations into an algebraic linear system of equations allows the successive calculation of the Taylor series coefficients up to an arbitrary order. The evaluation of the solution space reveals the wide range of possible lens configurations covered by this analytic design method. Ray tracing analysis for calculated 20th order Taylor polynomials demonstrate excellent performance and the versatility of this new analytical optics design concept.

Analytic free-form lens design for imaging applications with high aspect ratio

A new three-dimensional analytic optics design method is presented that enables the coupling of three ray sets with only two free-form lens surfaces. Closely related to the Simultaneous Multiple Surface method in three dimensions (SMS3D), it is derived directly from Fermat?s principle, leading to multiple sets of functional differential equations. The general solution of these equations makes it possible to calculate more than 80 coefficients for each implicit surface function. Ray tracing simulations of these free-form lenses demonstrate superior imaging performance for applications with high aspect ratio, compared to conventional rotational symmetric systems.

Analytic free-form lens design in 3D: coupling three ray sets using two lens surfaces

The two-dimensional analytic optics design method presented in a previous paper [Opt. Express 20, 5576–5585 (2012)] is extended in this work to the three-dimensional case, enabling the coupling of three ray sets with two free-form lens surfaces. Fermat’s principle is used to deduce additional sets of functional differential equations which make it possible to calculate the lens surfaces. Ray tracing simulations demonstrate the excellent imaging performance of the resulting free-form lenses described by more than 100 coefficients.

Analytic free-form lens design for tracking integration in concentrating photovoltaics

In this work the concept of tracking integration in concentrating photovoltaics (CPV) is revisited and developed further. With respect to conventional CPV, tracking integration eliminates the clear separation between stationary units of optics and solar cells, and external solar trackers. This approach is capable of further increasing the concentration ratio and makes high concentrating photovoltaics (> 500x) available for single-axis tracker installations. The reduced external solar tracking effort enables possibly cheaper and more compact installations. Our proposed optical system uses two laterally moving plano-convex lenses to achieve high concentration over a wide angular range of ±24°. The lateral movement allows to combine both steering and concentration of the incident direct sun light. Given the specific symmetry conditions of the underlying optical design problem, rotational symmetric lenses are not ideal for this application. For this type of design problems, a new free-form optics design method presented in previous papers perfectly matches the symmetry. It is derived directly from Fermat's principle, leading to sets of functional differential equations allowing the successive calculation of the Taylor series coeficients of each implicit surface function up to very high orders. For optical systems designed for wide field of view and with clearly separated optical surfaces, this new analytic design method has potential application in both fields of nonimaging and imaging optics.

Progress in the SMS design method for imaging optics

In this work, two SMS algorithms are presented for an objective design with different selected ray-bundles: three meridian ray-bundles (3M) and one meridian and two skew ray-bundles (1M-2S), the latter from pin hole point of view, provides a better sampling of the phase space. Results obtained with different algorithms will be compared

Advances in the Simultaneous Multiple Surface optical design method for imaging and non-imaging applications

Classical imaging optics has been developed over centuries in many areas, such as its paraxial imaging theory and practical design methods like multi-parametric optimization techniques. Although these imaging optical design methods can provide elegant solutions to many traditional optical problems, there are more and more new design problems, like solar concentrator, illumination system, ultra-compact camera, etc., that require maximum energy transfer efficiency, or ultra-compact optical structure. These problems do not have simple solutions from classical imaging design methods, because not only paraxial rays, but also non-paraxial rays should be well considered in the design process. Non-imaging optics is a newly developed optical discipline, which does not aim to form images, but to maximize energy transfer efficiency. One important concept developed from non-imaging optics is the “edge-ray principle”, which states that the energy flow contained in a bundle of rays will be transferred to the target, if all its edge rays are transferred to the target. Based on that concept, many CPC solar concentrators have been developed with efficiency close to the thermodynamic limit. When more than one bundle of edge-rays needs to be considered in the design, one way to obtain solutions is to use SMS method. SMS stands for Simultaneous Multiple Surface, which means several optical surfaces are constructed simultaneously. The SMS method was developed as a design method in Non-imaging optics during the 90s. The method can be considered as an extension to the Cartesian Oval calculation. In the traditional Cartesian Oval calculation, one optical surface is built to transform an input wave-front to an out-put wave-front. The SMS method however, is dedicated to solve more than 1 wave-fronts transformation problem. In the beginning, only 2 input wave-fronts and 2 output wave-fronts transformation problem was considered in the SMS design process for rotational optical systems or free-form optical systems. Usually “SMS 2D” method stands for the SMS procedure developed for rotational optical system, and “SMS 3D” method for the procedure for free-form optical system. Although the SMS method was originally employed in non-imaging optical system designs, it has been found during this thesis that with the improved capability to design more surfaces and control more input and output wave-fronts, the SMS method can also be applied to imaging system designs and possesses great advantage over traditional design methods. In this thesis, one of the main goals to achieve is to further develop the existing SMS-2D method to design with more surfaces and improve the stability of the SMS-2D and SMS-3D algorithms, so that further optimization process can be combined with SMS algorithms. The benefits of SMS plus optimization strategy over traditional optimization strategy will be explained in details for both rotational and free-form imaging optical system designs. Another main goal is to develop novel design concepts and methods suitable for challenging non-imaging applications, e.g. solar concentrator and solar tracker. This thesis comprises 9 chapters and can be grouped into two parts: the first part (chapter 2-5) contains research works in the imaging field, and the second part (chapter 6-8) contains works in the non-imaging field. In the first chapter, an introduction to basic imaging and non-imaging design concepts and theories is given. Chapter 2 presents a basic SMS-2D imaging design procedure using meridian rays. In this chapter, we will set the imaging design problem from the SMS point of view, and try to solve the problem numerically. The stability of this SMS-2D design procedure will also be discussed. The design concepts and procedures developed in this chapter lay the path for further improvement. Chapter 3 presents two improved SMS 3 surfaces’ design procedures using meridian rays (SMS-3M) and skew rays (SMS-1M2S) respectively. The major improvement has been made to the central segments selections, so that the whole SMS procedures become more stable compared to procedures described in Chapter 2. Since these two algorithms represent two types of phase space sampling, their image forming capabilities are compared in a simple objective design. Chapter 4 deals with an ultra-compact SWIR camera design with the SMS-3M method. The difficulties in this wide band camera design is how to maintain high image quality meanwhile reduce the overall system length. This interesting camera design provides a playground for the classical design method and SMS design methods. We will show designs and optical performance from both classical design method and the SMS design method. Tolerance study is also given as the end of the chapter. Chapter 5 develops a two-stage SMS-3D based optimization strategy for a 2 freeform mirrors imaging system. In the first optimization phase, the SMS-3D method is integrated into the optimization process to construct the two mirrors in an accurate way, drastically reducing the unknown parameters to only few system configuration parameters. In the second optimization phase, previous optimized mirrors are parameterized into Qbfs type polynomials and set up in code V. Code V optimization results demonstrates the effectiveness of this design strategy in this 2-mirror system design. Chapter 6 shows an etendue-squeezing condenser optics, which were prepared for the 2010 IODC illumination contest. This interesting design employs many non-imaging techniques such as the SMS method, etendue-squeezing tessellation, and groove surface design. This device has theoretical efficiency limit as high as 91.9%. Chapter 7 presents a freeform mirror-type solar concentrator with uniform irradiance on the solar cell. Traditional parabolic mirror concentrator has many drawbacks like hot-pot irradiance on the center of the cell, insufficient use of active cell area due to its rotational irradiance pattern and small acceptance angle. In order to conquer these limitations, a novel irradiance homogenization concept is developed, which lead to a free-form mirror design. Simulation results show that the free-form mirror reflector has rectangular irradiance pattern, uniform irradiance distribution and large acceptance angle, which confirm the viability of the design concept. Chapter 8 presents a novel beam-steering array optics design strategy. The goal of the design is to track large angle parallel rays by only moving optical arrays laterally, and convert it to small angle parallel output rays. The design concept is developed as an extended SMS method. Potential applications of this beam-steering device are: skylights to provide steerable natural illumination, building integrated CPV systems, and steerable LED illumination. Conclusion and future lines of work are given in Chapter 9. Resumen La óptica de formación de imagen clásica se ha ido desarrollando durante siglos, dando lugar tanto a la teoría de óptica paraxial y los métodos de diseño prácticos como a técnicas de optimización multiparamétricas. Aunque estos métodos de diseño óptico para formación de imagen puede aportar soluciones elegantes a muchos problemas convencionales, siguen apareciendo nuevos problemas de diseño óptico, concentradores solares, sistemas de iluminación, cámaras ultracompactas, etc. que requieren máxima transferencia de energía o dimensiones ultracompactas. Este tipo de problemas no se pueden resolver fácilmente con métodos clásicos de diseño porque durante el proceso de diseño no solamente se deben considerar los rayos paraxiales sino también los rayos no paraxiales. La óptica anidólica o no formadora de imagen es una disciplina que ha evolucionado en gran medida recientemente. Su objetivo no es formar imagen, es maximazar la eficiencia de transferencia de energía. Un concepto importante de la óptica anidólica son los “rayos marginales”, que se pueden utilizar para el diseño de sistemas ya que si todos los rayos marginales llegan a nuestra área del receptor, todos los rayos interiores también llegarán al receptor. Haciendo uso de este principio, se han diseñado muchos concentradores solares que funcionan cerca del límite teórico que marca la termodinámica. Cuando consideramos más de un haz de rayos marginales en nuestro diseño, una posible solución es usar el método SMS (Simultaneous Multiple Surface), el cuál diseña simultáneamente varias superficies ópticas. El SMS nació como un método de diseño para óptica anidólica durante los años 90. El método puede ser considerado como una extensión del cálculo del óvalo cartesiano. En el método del óvalo cartesiano convencional, se calcula una superficie para transformar un frente de onda entrante a otro frente de onda saliente. El método SMS permite transformar varios frentes de onda de entrada en frentes de onda de salida. Inicialmente, sólo era posible transformar dos frentes de onda con dos superficies con simetría de rotación y sin simetría de rotación, pero esta limitación ha sido superada recientemente. Nos referimos a “SMS 2D” como el método orientado a construir superficies con simetría de rotación y llamamos “SMS 3D” al método para construir superficies sin simetría de rotación o free-form. Aunque el método originalmente fue aplicado en el diseño de sistemas anidólicos, se ha observado que gracias a su capacidad para diseñar más superficies y controlar más frentes de onda de entrada y de salida, el SMS también es posible aplicarlo a sistemas de formación de imagen proporcionando una gran ventaja sobre los métodos de diseño tradicionales. Uno de los principales objetivos de la presente tesis es extender el método SMS-2D para permitir el diseño de sistemas con mayor número de superficies y mejorar la estabilidad de los algoritmos del SMS-2D y SMS-3D, haciendo posible combinar la optimización con los algoritmos. Los beneficios de combinar SMS y optimización comparado con el proceso de optimización tradicional se explican en detalle para sistemas con simetría de rotación y sin simetría de rotación. Otro objetivo importante de la tesis es el desarrollo de nuevos conceptos de diseño y nuevos métodos en el área de la concentración solar fotovoltaica. La tesis está estructurada en 9 capítulos que están agrupados en dos partes: la primera de ellas (capítulos 2-5) se centra en la óptica formadora de imagen mientras que en la segunda parte (capítulos 6-8) se presenta el trabajo del área de la óptica anidólica. El primer capítulo consta de una breve introducción de los conceptos básicos de la óptica anidólica y la óptica en formación de imagen. El capítulo 2 describe un proceso de diseño SMS-2D sencillo basado en los rayos meridianos. En este capítulo se presenta el problema de diseñar un sistema formador de imagen desde el punto de vista del SMS y se intenta obtener una solución de manera numérica. La estabilidad de este proceso se analiza con detalle. Los conceptos de diseño y los algoritmos desarrollados en este capítulo sientan la base sobre la cual se realizarán mejoras. El capítulo 3 presenta dos procedimientos para el diseño de un sistema con 3 superficies SMS, el primero basado en rayos meridianos (SMS-3M) y el segundo basado en rayos oblicuos (SMS-1M2S). La mejora más destacable recae en la selección de los segmentos centrales, que hacen más estable todo el proceso de diseño comparado con el presentado en el capítulo 2. Estos dos algoritmos representan dos tipos de muestreo del espacio de fases, su capacidad para formar imagen se compara diseñando un objetivo simple con cada uno de ellos. En el capítulo 4 se presenta un diseño ultra-compacto de una cámara SWIR diseñada usando el método SMS-3M. La dificultad del diseño de esta cámara de espectro ancho radica en mantener una alta calidad de imagen y al mismo tiempo reducir drásticamente sus dimensiones. Esta cámara es muy interesante para comparar el método de diseño clásico y el método de SMS. En este capítulo se presentan ambos diseños y se analizan sus características ópticas. En el capítulo 5 se describe la estrategia de optimización basada en el método SMS-3D. El método SMS-3D calcula las superficies ópticas de manera precisa, dejando sólo unos pocos parámetros libres para decidir la configuración del sistema. Modificando el valor de estos parámetros se genera cada vez mediante SMS-3D un sistema completo diferente. La optimización se lleva a cabo variando los mencionados parámetros y analizando el sistema generado. Los resultados muestran que esta estrategia de diseño es muy eficaz y eficiente para un sistema formado por dos espejos. En el capítulo 6 se describe un sistema de compresión de la Etendue, que fue presentado en el concurso de iluminación del IODC en 2010. Este interesante diseño hace uso de técnicas propias de la óptica anidólica, como el método SMS, el teselado de las lentes y el diseño mediante grooves. Este dispositivo tiene un límite teórica en la eficiencia del 91.9%. El capítulo 7 presenta un concentrador solar basado en un espejo free-form con irradiancia uniforme sobre la célula. Los concentradores parabólicos tienen numerosas desventajas como los puntos calientes en la zona central de la célula, uso no eficiente del área de la célula al ser ésta cuadrada y además tienen ángulos de aceptancia de reducido. Para poder superar estas limitaciones se propone un novedoso concepto de homogeneización de la irrandancia que se materializa en un diseño con espejo free-form. El análisis mediante simulación demuestra que la irradiancia es homogénea en una región rectangular y con mayor ángulo de aceptancia, lo que confirma la viabilidad del concepto de diseño. En el capítulo 8 se presenta un novedoso concepto para el diseño de sistemas afocales dinámicos. El objetivo del diseño es realizar un sistema cuyo haz de rayos de entrada pueda llegar con ángulos entre ±45º mientras que el haz de rayos a la salida sea siempre perpendicular al sistema, variando únicamente la posición de los elementos ópticos lateralmente. Las aplicaciones potenciales de este dispositivo son varias: tragaluces que proporcionan iluminación natural, sistemas de concentración fotovoltaica integrados en los edificios o iluminación direccionable con LEDs. Finalmente, el último capítulo contiene las conclusiones y las líneas de investigación futura.

Analysis of Super Imaging Properties of Spherical Geodesic Waveguide Using COMSOL Multyphisics

Negative Refractive Lens (NRL) has shown that an optical system can produce images with details below the classic Abbe diffraction limit using materials of negative dielectric and magnetic constants. Recently, two devices with positive refraction, the Maxwell Fish Eye lens (MFE) (Leonhardt et al 2000) and the Spherical Geodesic Waveguide (SGW)(Minano et all 2011) have been claimed to break the diffraction limit using positive refraction with a different meaning. In these cases, it has been considered the power transmission from a point source to a point receptor, which falls drastically when the receptor is displaced from the focus by a distance much smaller than the wavelength. Moreover, recent analysis of the SGW with defined object and image surfaces, which are both conical sections of the sphere, has shown that the system transmits images bellow diffraction limit. The key assumption is the use of a perfectly absorbing receptor called perfect drain. This receptor is capable to absorb all the radiation without reflection or scattering. Here, it is presented the COMSOL analysis of the SGW using a perfect drain that absorbs perfectly two modes. The design procedure for PD capable to absorb k modes is proposed, as well.

Perfect imaging analysis of the spherical geodesic waveguide

Negative Refractive Lens (NRL) has shown that an optical system can produce images with details below the classic Abbe diffraction limit. This optical system transmits the electromagnetic fields, emitted by an object plane, towards an image plane producing the same field distribution in both planes. In particular, a Dirac delta electric field in the object plane is focused without diffraction limit to the Dirac delta electric field in the image plane. Two devices with positive refraction, the Maxwell Fish Eye lens (MFE) and the Spherical Geodesic Waveguide (SGW) have been claimed to break the diffraction limit using positive refraction with a different meaning. In these cases, it has been considered the power transmission from a point source to a point receptor, which falls drastically when the receptor is displaced from the focus by a distance much smaller than the wavelength. Although these systems can detect displacements up to ?/3000, they cannot be compared to the NRL, since the concept of image is different. The SGW deals only with point source and drain, while in the case of the NRL, there is an object and an image surface. Here, it is presented an analysis of the SGW with defined object and image surfaces (both are conical surfaces), similarly as in the case of the NRL. The results show that a Dirac delta electric field on the object surface produces an image below the diffraction limit on the image surface.