The automated design of imaging systems involving no or minimal human effort has always been the expectation of scientists, researchers and optical engineers. In addition, it is challenging to choose an appropriate starting point for an optical system design. In this paper, we present a novel design framework based on a point-by-point design process that can automatically obtain high-performance freeform systems. This framework only requires a combination of planes as the input based on the configuration requirements or the prior knowledge of designers. This point-by-point design framework is different from the decades-long tradition of optimizing surface coefficients. Compared with the traditional design method, whereby the selection of the starting point and the optimization process are independent of each other and require extensive amount of human effort, there are no obvious differences between these two processes in our design framework, and the entire design process is mostly automated. This automated design process significantly reduces the amount of human effort required and does not rely on advanced design skills and experience. To demonstrate the feasibility of the proposed design framework, we successfully designed two high-performance systems as examples. This point-by-point design framework opens up new possibilities for automated optical design and can be used to develop automated optical design in the areas of remote sensing, telescopy, microscopy, spectroscopy, virtual reality and augmented reality.

Automated design of freeform imaging systems.

In this paper, we proposed a general direct design method for three-dimensional freeform surfaces and freeform imaging systems based on a construction-iteration process. In the preliminary surfaces-construction process, the coordinates as well as the surface normals of the data points on the multiple freeform surfaces can be calculated directly considering the rays of multiple fields and different pupil coordinates. Then, an iterative process is employed to significantly improve the image quality or achieve a better mapping relationship of the light rays. Three iteration types which are normal iteration, negative feedback and successive approximation are given. The proposed construction-iteration method is applied in the design of an easy aligned, low F-number off-axis three-mirror system. The primary and tertiary mirrors can be fabricated on a single substrate and form a single element in the final system. The secondary mirror is simply a plane mirror. With this configuration, the alignment difficulty of a freeform system can be greatly reduced. After the preliminary surfaces-construction stage, the freeform surfaces in the optical system can be generated directly from an initial planar system. Then, with the iterative process, the average RMS spot diameter decreased by 75.4% compared with the system before iterations, and the maximum absolute distortion decreased by 94.2%. After further optimization with optical design software, good image quality which is closed to diffraction-limited is achieved.

Direct design of freeform surfaces and freeform imaging systems with a point-by-point three-dimensional construction-iteration method.

Head-mounted display (HMD) has been widely used in many fields, and most existing HMDs are complex and typically non-aesthetically pleasing. In this paper, a novel compact, lightweight and wearable off-axis HMD with freeform surface is reported. It is challenging to achieve large field of view (FOV) and maintain compact structure simultaneously for this type system. In this design, the compact off-axis HMD consists of a tilted ellipsoid combiner and a four pieces relay lenses. It offers a diagonal FOV of 30°, and an exit pupil diameter of 7 mm. No diffractive surfaces are used, thus avoiding the effect of stray light and ghost image in previous designs. The x-y polynomial freeform surface is adopted in the relay lens for improving the image quality and minimizing the structure size. Analytical expressions to determine the initial structure of HMD has been given, while structure constrains, optimization strategy and tolerance analysis are also described in details. The optical system is easy to manufacture by ordinary method which is beneficial for mass production. Further, a prototype of this compact HMD is successfully implemented with good imaging performance. The compact structure of HMD makes it well suited for integrating a normal glass, significantly advancing the application of HMD in people’s daily life.

Design and fabrication of a compact off-axis see-through head-mounted display using a freeform surface.

Measurement of Freeform Optical Surfaces: Trade‐Off between Accuracy and Dynamic Range

Cellphones equipped with high-quality cameras and powerful CPUs as well as GPUs are widespread. This opens new prospects to use such existing computational and imaging resources to perform medical diagnosis in developing countries at a very low cost. Many relevant samples, like biological cells or waterborn parasites, are almost fully transparent. As they do not exhibit absorption, but alter the light's phase only, they are almost invisible in brightfield microscopy. Expensive equipment and procedures for microscopic contrasting or sample staining often are not available. Dedicated illumination approaches, tailored to the sample under investigation help to boost the contrast. This is achieved by a programmable illumination source, which also allows to measure the phase gradient using the differential phase contrast (DPC) [1, 2] or even the quantitative phase using the derived qDPC approach [3]. By applying machine-learning techniques, such as a convolutional neural network (CNN), it is possible to learn a relationship between samples to be examined and its optimal light source shapes, in order to increase e.g. phase contrast, from a given dataset to enable real-time applications. For the experimental setup, we developed a 3D-printed smartphone microscope for less than 100 $ using off-the-shelf components only such as a low-cost video projector. The fully automated system assures true Koehler illumination with an LCD as the condenser aperture and a reversed smartphone lens as the microscope objective. We show that the effect of a varied light source shape, using the pre-trained CNN, does not only improve the phase contrast, but also the impression of an improvement in optical resolution without adding any special optics, as demonstrated by measurements.

/pdf/using-machine-learning-to-optimize-phase-contrast-in-a-low-4un2pfxgrf.pdf

Using machine-learning to optimize phase contrast in a low-cost cellphone microscope.

In this paper, we have proposed an approach that utilizes freeform optical surfaces to realize a novel optical function called transverse image translation, which acts as a basic geometrical transformation for images. Its purpose is to make the image of a given optical system move directionally with the designated distance by means of inserting and arranging some extra optical elements behind the given system. The structure of the given system, as well as its optical specifications, stays unchanged when performing the translation. As the translation is transverse, the image can only move transversely in the plane where the original image lies. A freeform single lens comprising two different freeform surfaces is designed for the given system as the only translation element. The image of the given system is expected to be successfully translated transversely as designed when the freeform lens is properly inserted. The design method and process of the freeform lens is presented briefly. Additionally, a design example is introduced to demonstrate the feasibility of our proposed approach for this new type of transverse image translation.

Transverse image translation using an optical freeform single lens.

The manufacture of high-precision surfaces is the foundation of building high-performance optical systems. For over 50 years, the tolerance for optical surfaces has been specified by the root-mean-square (rms) or peak-to-valley (PV) value over the entire surface geometry. However, different regions on optical surfaces do not contribute equally to image quality and, thus, can tolerate different levels of errors. A global tolerance described by a single or few parameters cannot precisely provide the manufacturing requirements of each region on the surface, which may result in unnecessary accuracy specifications for surfaces. Furthermore, the components with the same PV or rms figure errors can produce different imaging qualities; however, this difference cannot be distinguished by the conventional figure of merit. To address these problems, a framework that includes a local tolerance model and a quality merit function for optical surfaces is proposed. The local tolerance model can provide an accurate tolerance for each region on the surface so the targeted wave aberration requirements are met during components manufacturing. More importantly, the proposed merit function closely ties the surface figure error to imaging performance, e.g., the findings can explain that the component with lower geometric accuracy may produce better imaging quality. This framework provides new insights into optical design, manufacture, and metrology and especially paves the way for the manufacture of high-precision large-aperture systems. 

Local surface tolerance and quality evaluation of optical surfaces

In this paper, we have proposed an innovative model of freeform illumination design, which differs from the current model that covers almost all of the existing freeform illumination systems. In our model, a freeform illumination system is designed for multiple light sources simultaneously, rather than just for one certain source like the current model. All the sources have the same size, shape, intensity distribution, and other photometric characteristics, but are located at different positions or directions. Each source can individually achieve an illumination pattern on the target plane. All the patterns are expected to have the same size, shape, and illuminance distribution, but the position of each pattern has a linear relationship with the position or direction of the corresponding source. Two new (to our knowledge) illumination functions can be realized in our model, as the light sources are non-single and movable. The first one is the continuous scanning of the illumination pattern on the target plane, and the second one achieves a flexible, diverse, and controllable array of illumination patterns on the target plane. As an example, a coaxial freeform illumination system has been designed under the framework of this model, in which multiple collimated light sources are introduced simultaneously. The design method and process of the system are presented. The system is further promoted, and the two new illumination functions are explained in detail based on the design example.

Freeform illumination design model for multiple light sources simultaneously

In this paper, we demonstrated the design method of freeform unobscured reflective imaging systems using the point-bypoint Construction-Iteration (CI) method. Compared with other point-by-point design methods, the light rays of multiple fields and different pupil coordinates are employed in the design. The whole design process starts from a simple initial system consisting of decentered and tilted planes. In the preliminary surfaces-construction stage, the coordinates as well as the surface normals of the feature data points on each freeform surface can be calculated point-by-point directly based on the given object-image relationships. Then, the freeform surfaces are generated through a novel surface fitting method considering both the coordinates and surface normals of the data points. Next, an iterative process is employed to significantly improve the image quality. In this way, an unobscured design with freeform surfaces can be obtained directly, and it can be taken as a good starting point for further optimization. The benefit and feasibility of this design method is demonstrated by two design examples of high-performance freeform unobscured imaging systems. Both two systems have good imaging performance after final design.

Design of freeform unobscured reflective imaging systems using CI method

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