Unobscured reflective systems can also be applied in infrared region for higher image quality and optical efficiency. For infrared reflective systems, the signal noise ratio (SNR) is a critical parameter, which would be influenced by the F-number and the external thermal radiation. To suppress these stray lights, a common method is that the cold stop of the infrared detector matches the entrance pupil of the optical system. But the cooled mid-infrared unobscured system is difficult to design due to the asymmetrical structure. Freeform surfaces provide designers more flexibility with respect to the aberration correction in the optimal design process, which have been widely applied to reduce the optical system volume and improve the imaging performance. Within this article, a cooled mid-infrared three-mirror (CMT) system with an intermediate image plane using freeform surfaces is presented. In Section 2, the optical and mechanical designs are thoroughly discussed, including the selection of initial structure and the optimization of freeform surfaces. The imaging performance and stray light analysis would be conducted to verify the cold stop efficiency of this system. In Section 3, this system assembly and performance test are implemented, which will verify machining precision of these reflectors and this design system feasibility at the infrared application.
Head-mounted display (HMD) system is a research hotspot in virtual reality, which has continuous and rapid development in training, medical treatment, aerospace, and entertainment. For the more comfortable immersive experience, the requirements of compact structure, large exit pupil and low F number should be met simultaneously in HMD system. With the use of x-y polynomial surface, an off-axis head-mounted display system with two freeform reflectors is achieved. The HMD system demonstrates a 10 mm exit pupil, a 23°×16° field of view, an f/# number of 3.0 and an eye relief larger than 15 mm. Based on the tolerance analysis of surface figure errors and position location, we present the on-machine measurement and compensation for enhancing machining accuracy, and the frame and mirror integration for high assembling accuracy. Finally, the HMD system was fabricated and the imaging quality was evaluated. In comparison with the results, the effectiveness of the on-machine measurement and compensation are validated, as well as the reliability of tolerance analysis and mechanical structure.
Modern advanced manufacturing and testing technologies allow the application of freeform optical elements. Compared with traditional spherical surfaces, an optical freeform surface has more degrees of freedom in optical design and provides substantially improved imaging performance. In freeform optics, the representation technique of a freeform surface has been a fundamental and key research topic in recent years. Moreover, it has a close relationship with other aspects of the design, manufacturing, testing, and application of optical freeform surfaces. Improvements in freeform surface representation techniques will make a significant contribution to the further development of freeform optics. We present a detailed review of the different types of optical freeform surface representation techniques and their applications and discuss their properties and differences. Additionally, we analyze the future trends of optical freeform surface representation techniques.
A combination method using numerical orthogonal polynomials and overlapping averaging is presented for freeform surface estimation. The whole effective aperture of freeform surface is decomposed into multiple overlapped subapertures. The corresponding local surface over each subaperture is reconstructed by numerical orthogonal polynomials suited for general shaped aperture. Then, the whole freeform surface is obtained by overlapping averaging approach from multiple local surfaces. The performance of the presented combination method is discussed and demonstrated by examples and further verified by an experiment. The results show that the combination method could reach nanometer accuracy. Meanwhile, the local deformations of freeform surface can be characterized finely.
A white-light microscopy interferometer was developed for measurement of the 3D profile and roughness.10X, 20X and 50X Mirau interference microscope objectives with the numerical aperture of 0.3, 0.4 and 0.55 were designed, manufactured and then provided as the accessories. Thickness deviation between beam splitter plate and reference mirror plate as well as the numerical aperture will both affect the contrast of interference fringe, according to optical modeling and image evaluation. The former would generate dispersion and then decrease the fringe contrast, while the latter would not produce dispersion separately but impact the amount of dispersion when thickness deviation exists, and their influence on fringe contrast was based on the expression of white-light interference intensity. Simulations for interference fringes from Mirau interference microscope objectives with different NA and thickness deviation were implemented, demonstrated that the fringe contrast will be falling with NA and thickness deviation increasing. A standard step with the nominal step value of 110 nm was used to calibrate the white-light microscopy interferometer, showing that less than1nm deviation can be reached.
In practical optical measurements, the wavefront data are recorded by pixelated imaging sensors. The closed-form analytical base polynomial will lose its orthogonality in the discrete wavefront database. For a wavefront with an irregularly shaped aperture, the corresponding analytical base polynomials are laboriously derived. The use of numerical orthogonal polynomials for reconstructing a wavefront with a general shaped aperture over the discrete data points is presented. Numerical polynomials are orthogonal over the discrete data points regardless of the boundary shape of the aperture. The performance of numerical orthogonal polynomials is confirmed by theoretical analysis and experiments. The results demonstrate the adaptability, validity, and accuracy of numerical orthogonal polynomials for estimating the wavefront over a general shaped aperture from regular boundary to an irregular boundary.
Freeform complex surfaces with steep variations in local areas cannot be fitted by analytical functions with high accuracy in the whole aperture in optics. A framework with a combination of Zernike polynomials as base function with radial basis function method is presented to improve reconstruction accuracy for freeform complex surfaces with circular aperture. The algorithm of the framework is analyzed, and the performance of the method is investigated and verified by numerical experiments. The proposed method is accurate and highly adaptable, which could be applied in modern optical manufacturing and measurement.
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