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Coherence scanning interferometry (CSI) is a widely used non-contact method for measuring areal surface topography. The calculation of groove depth typically employs the ‘W/3 rule’ specified in ISO 5436-1. However, the batwing effect causes overshoots near the groove edges, which can introduce noise singularities in the selected W/3 region for depth calculation, thereby affecting the measurement of rectangular grating depth. This paper introduces the definition of batwing height and width and proposes a simulation model that considers various factors, such as the center wavelength, spectrum of the illuminating light, shadow effect, and numerical aperture, to analyze their influence on depth measurement. The simulation results demonstrate that the batwing width is the primary factor influencing depth measurement for small grating periods. Specifically, a decrease in numerical aperture increases the batwing width, leading to larger depth measurement errors, while a decrease in the center wavelength reduces the batwing width, resulting in smaller depth measurement errors. The influence of the illumination spectrum and shadow effect on depth measurement is found to be minor. Experimental validation using a step standard consisting of rectangular gratings with different periods and depths confirms the agreement between the experimental and simulated results. The proposed method provides a quantitative evaluation of depth measurement accuracy in CSI.

In this paper, a direct design method for an off-axis two-mirror telecentric scanning system with a linear field of view (FOV) is proposed. A single freeform mirror structure is firstly considered, in which the aberration free geometry of the off-axis parabolic (OAP) surface is leveraged to provide the focusing function and build surface contour of the sub-region on the mirror for each FOV. Multiple OAP surfaces for construction of the freeform mirror are located at an OAP base to satisfy the telecentric condition. The imaging distortion of this single freeform mirror structure is analyzed and found unavoidable due to the unsymmetrical geometry of the OAP base. A freeform reflective corrector is supplemented, and it is constructed from multiple plane surfaces located at a curved base to fulfill the f-theta scanning geometry. Thus, a two-mirror structure composed of one freeform primary mirror and one freeform reflective corrector is established. Each plane-OAP surfaces pair corresponds to a specific FOV. These multiple OAP surfaces and multiple plane surfaces are then expanded and mixed respectively, to construct the freeform primary mirror and freeform reflective corrector. An f-theta two-mirror freeform scanning system with ±10.4° linear FOV is designed using the proposed construction method. The design result is diffraction-limited, and a scanning error less than 5 μm and telecentricity angle less than 0.2° are achieved.

To construct a life-sized eye model using the three-dimensional (3D) printing technology for fundus viewing study of the viewing system.We devised our schematic model eye based on Navarro's eye and redesigned some parameters because of the change of the corneal material and the implantation of intraocular lenses (IOLs). Optical performance of our schematic model eye was compared with Navarro's schematic eye and other two reported physical model eyes using the ZEMAX optical design software. With computer aided design (CAD) software, we designed the 3D digital model of the main structure of the physical model eye, which was used for three-dimensional (3D) printing. Together with the main printed structure, polymethyl methacrylate(PMMA) aspherical cornea, variable iris, and IOLs were assembled to a physical eye model. Angle scale bars were glued from posterior to periphery of the retina. Then we fabricated other three physical models with different states of ammetropia. Optical parameters of these physical eye models were measured to verify the 3D printing accuracy.In on-axis calculations, our schematic model eye possessed similar size of spot diagram compared with Navarro's and Bakaraju's model eye, much smaller than Arianpour's model eye. Moreover, the spherical aberration of our schematic eye was much less than other three model eyes. While in off- axis simulation, it possessed a bit higher coma and similar astigmatism, field curvature and distortion. The MTF curves showed that all the model eyes diminished in resolution with increasing field of view, and the diminished tendency of resolution of our physical eye model was similar to the Navarro's eye. The measured parameters of our eye models with different status of ametropia were in line with the theoretical value.The schematic eye model we designed can well simulate the optical performance of the human eye, and the fabricated physical one can be used as a tool in fundus range viewing research.

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

An absolute testing method for cylindrical surfaces is presented in a null test setup with a computergenerated hologram. The absolute test exploits the symmetry of cylinders, which allows us to introduce a certain shift of the test surface both parallel to and rotated about the centerline while the null test condition is still maintained. With two shifts of the cylindrical surface, four measurements belonging to two groups in conjugate positions can be accomplished to obtain the absolute differential map with the interferometer and null optics errors removed. The absolute surface can be obtained by wavefront reconstruction from local differential data. A simulation of the method is presented to estimate the error propagation. Experimental absolute test results of a concave cylindrical surface with 100-mm radius are given. The measured profiles are compared with those obtained from a commercial profiler, showing a difference of less than 15 nm (root-mean-square). [ABSTRACT FROM AUTHOR]

A new ultra-wide-angle projection function called fovea-stereographic is described and characterized by the relative relationship between the radial distortion level and the object field-of-view (FOV) angle, creating a high-resolution wide foveal image and adequate peripheral information to be processed within a limited computational time. The paper also provides the design results of an innovative fast fovea-stereographic fisheye lens system with a 170 deg of FOV that shows a more than 58.8% (100 deg) high-resolution central foveal image and at least 15% more peripheral information than any other light projection. Our lens distortion curve, in addition to its modulation transfer function, produces a high-resolution projection for real-time tracking and image transmission applications. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Three important parts of a portable phase-shifting interferometer with optical zoom system are described. The first is a phase-shifter whose driver is integrated in small size with milli-voltage resolution and kHz dynamic-frequency response. Second, a seed-algorithm is proposed that some spatial points are picked up as seeds, and the wavefronts with obscuration or irregular edges can be retrieved from these seeds as they grow and spread. Third, the measurement of a corner-cube reflector is given in detail. © 2004 Wiley Periodicals, Inc. Microwave Opt Technol Lett 43: 417–419, 2004; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.20487 [ABSTRACT FROM AUTHOR]

In an amplitude grating system of small grid pitch, the diffractive effect is distinctive. Its energy will be about 10–40% of the total energy. The diffractive light is the root cause of deterioration of the contrast and sinusoidal property of the Moiré signal. The relations between the phase of ± first-order Moiré fringes and other factors, such as the gap of the grating pair, are analyzed. It is proposed to use ± first-order Moiré fringes to obtain high-quality signals. © 2001 John Wiley & Sons, Inc. Microwave Opt Technol Lett 31: 91–93, 2001. [ABSTRACT FROM AUTHOR]

Partial null interferometry without using any null optics is proposed to measure a concave freeform Zernike mirror. Oblique incidence on the freeform mirror is used to compensate for astigmatism as the main component in its figure, and to constrain the divergence of the test beam as well. The phase demodulated from the partial nulled interferograms is divided into low-frequency phase and high-frequency phase by Zernike polynomial fitting. The low-frequency surface figure error of the freeform mirror represented by the coefficients of Zernike polynomials is reconstructed from the low-frequency phase, applying the reverse optimization reconstruction technology in the accurate model of the interferometric system. The high-frequency surface figure error of the freeform mirror is retrieved from the high-frequency phase adopting back propagating technology, according to the updated model in which the low-frequency surface figure error has been superimposed on the sag of the freeform mirror. Simulations verified that this method is capable of testing a wide variety of astigmatism-dominated freeform mirrors due to the high dynamic range. The experimental result using our proposed method for a concave freeform Zernike mirror is consistent with the null test result employing the computer-generated hologram. [ABSTRACT FROM AUTHOR]

Simultaneous dual-wavelength interferometry (SDWI) could extend the measured range of each single-wavelength interferometry. The moiré fringe generated in SDWI indirectly represents the information of the measured long synthetic-wavelength phase, thus the phase demodulation is rather arduous. To address this issue, we present a method to convert the moiré fringe pattern into a synthetic-wavelength interferogram (moiré to synthetic-wavelength, MTS). After the square of the moiré fringe pattern in the MTS method, the additive moiré pattern is turned into a multiplicative one. And the synthetic-wavelength interferogram could be obtained by a low-pass filtering in spectrum of the multiplicative moiré fringe pattern. Therefore, when the dual-wavelength interferometer is implemented with the π/2 phase shift at a sequence of synthetic-wavelength phase-shift interferograms with π/2 phase shift could be obtained after the MTS method processing on the captured moiré fringe patterns. And then the synthetic-wavelength phase could be retrieved by the conventional phase-shift algorithm. Compared with other methods in SDWI, the proposed MTS approach could reduce the restriction of the phase shift and frame numbers for the adoption of the conventional phase-shift algorithm. Following, numerical simulations are executed to evaluate the performance of the MTS method in processing time, frames of interferograms and the phase shift error compensation. And the necessary linear carrier for MTS method is less than 0.11 times of the traditional dual-wavelength spatial-domain Fourier transform method. Finally, the deviations for MTS method in experiment are 0.97% for a step with the height of 7.8 μm and 1.11% for a Fresnel lens with the step height of 6.2328 μm. [ABSTRACT FROM AUTHOR]