Cristina Canavesi

Observations on the linear programming formulation of the single reflector design problem.

We implemented the linear programming approach proposed by Oliker and by Wang to solve the single reflector problem for a point source and a far-field target. The algorithm was shown to produce solutions that aim the input rays at the intersections between neighboring reflectors. This feature makes it possible to obtain the same reflector with a low number of rays - of the order of the number of targets - as with a high number of rays, greatly reducing the computation complexity of the problem.

Target flux estimation by calculating intersections between neighboring conic reflector patches

We propose a fast algorithm to estimate the flux collected by conic reflector patches, based on the calculation of intersections between neighboring patches. The algorithm can be employed in conjunction with the supporting ellipsoids algorithm for freeform reflector design and is shown to be orders of magnitude faster and more scalable than the commonly used Monte Carlo ray tracing approach.

Illumination devices for photodynamic therapy of the oral cavity.

Three compact and efficient designs are proposed to deliver an average irradiance of 50 mW/cm2 with spatial uniformity well above 90% over a 25 mm2 target area for photodynamic therapy of the oral cavity. The main goal is to produce uniform illumination on the target while limiting irradiation of healthy tissue, thus overcoming the need of shielding the whole oral cavity and greatly simplifying the treatment protocol. The first design proposed consists of a cylindrical diffusing fiber placed in a tailored reflector derived from the edge-ray theorem with dimensions 5.5 × 7.2 × 10 mm3; the second device combines a fiber illuminator and a lightpipe with dimensions 6.8 × 6.8 × 50 mm3; the third design, inspired by the tailored reflector, is based on a cylindrical diffusing fiber and a cylinder reflector with dimensions 5 × 10 × 11 mm3. A prototype for the cylinder reflector was built that provided the required illumination for photodynamic therapy of the oral cavity, producing a spatial uniformity on the target above 94% and an average irradiance of 51 mW/cm2 for an input power of 70 mW.

Lightpipe device for delivery of uniform illumination for photodynamic therapy of the oral cavity

A compact and efficient lightpipe device to deliver light to the human oral cavity for photodynamic therapy was designed and fabricated, having dimensions 6.8u2009mm × 6.8u2009mm × 46u2009mm. An average irradiance of 76u2009mW/cm2 with an average deviation of 5% was measured on a square 25u2009mm2 treatment field for an input power of 100u2009mW. The device limits irradiation of healthy tissue and offers potential for improvement over the current treatment procedure, which requires shielding of the whole cavity to avoid damage to healthy tissue.

Direct calculation algorithm for two-dimensional reflector design

We have developed a fast algorithm to design two-dimensional reflector surfaces that ties together the supporting paraboloids, linear programming, and numerical integration methods. The algorithm builds upon the properties of conics and is shown to be several orders of magnitude faster than the supporting paraboloids and linear programming methods. The scalability and ease of implementation of the algorithm are discussed.

Design of a Retinal Tracking System for Jumping Spiders

We designed an optical system for tracking the retinal movement of a jumping spider as a stimulus is presented to it. The system, using all off-the-shelf optical components except for one custom aspheric plate, consists of three sub-systems that share a common path: a visible stimuli presentation sub-system, a NIR illumination sub-system, and a NIR retinal imaging sub-system. A 25 mm clearance between the last element and the spider ensures a stable positioning of the spider. The stimuli presentation system relays an image from a display to the spider eye, matching the 15 arcmin resolution of the two principal eyes and producing a virtual image at a distance of 255 mm from the spider, with a visual full field of view of 52°. When viewing a stimulus, the spider moves its retinas, which cover a full field of view of only 0.6°, and directs them to view different places in the visual field. The retinal imaging system uses a NIR camera to track changes of 0.5° in the field of view seen by the spider. By tracking retinal movement across images presented to spiders, we will learn how they search for visual cues to identify prey, rivals, and potential mates.

Design of illumination devices for delivery of photodynamic therapy in the oral cavity

We present three designs for delivery of light in the oral cavity for photodynamic therapy (PDT) under the requirements of average irradiance of 50 mW/cm2 and spatial non-uniformities well under 10% over a square area of 25 mm2. The main goal is to design a device that avoids having to shield the oral cavity prior to irradiation for PDT. Illumination theory is instrumental in identifying an effective geometry for the device. The designs proposed build upon the technology that is already available for PDT and use illumination theory concepts to maximize the efficiency of the light delivery. One design combines a cylindrical diffusing fiber with a reflector derived from the edge-ray theorem while a second consists of a fiber illuminator coupled to a lightpipe device. Both designs are successful in delivering the light reducing the need of shielding and in providing the desired irradiance and uniformity. The two approaches performed comparably and provided a higher irradiance than needed, thus inspiring the design of a third, simpler design based on an off-axis cylinder reflector.

Supporting conic design methods and conic intersection properties

Abstract. The supporting ellipsoids and linear programming reflector design methods build upon the property of conics to address the inverse problem of finding the freeform surface that directs light from a point source to produce a prescribed target distribution. We review the properties and main computational limitations of the two methods and show that a fast flux estimation method based on contour detection can be used in combination with the supporting ellipsoid algorithm. Once the intersections between neighboring conic patches on the reflector are known, it is possible to estimate the collected flux using the vertices of the intersection boundary. The advantage of using the intersection method to estimate the flux instead of the more common approach—Monte Carlo ray tracing—is that there is no tradeoff between speed and accuracy. Examples of flux estimation with the intersection method for different target configurations are shown.

Retinal imaging with virtual reality stimulus for studying Salticidae retinas

We present a 3-path optical system for studying the retinal movement of jumping spiders: a visible OLED virtual reality system presents stimulus, while NIR illumination and imaging systems observe retinal movement.

Implementation of the linear programming algorithm for freeform reflector design

We present observations on the linear programming algorithm proposed independently by Oliker and by Wang to design a single reflector for a point source and a far-field target. Given a set of source rays and discretized target intensities, the linear programming algorithm solves a variational problem to produce a reflector solution that consists of paraboloid patches. The computational complexity increases quadratically with the number of source rays and targets; this makes it important to minimize the number of source rays. However, minimizing the number of source rays results in solutions where the source rays at the intersection between neighboring patches split between multiple targets. This is unlike other discretized target reflector design methods, such as the Oliker supporting ellipsoid algorithm, that are used to aim numerous rays per ellipsoid at only one target. We uncovered a relationship between the optimal numbers of source rays and targets needed to run the problem. This relationship makes it possible to limit the number of source rays used in the design to the order of the number of target points. In this paper, we highlight the main features and current limitations of the linear programming algorithm. Finally, we propose a fast algorithm for 2D reflector design inspired by the intersection property of the linear programming method. The direct calculation method is shown to be several orders of magnitude faster than the linear programming method.