One of the new problems that has to be solved for segmented mirrors is related to periodic phasing, because for such mirrors to exhibit diffraction-limited performance the segments have to be positioned with an accuracy of a fraction of a wavelength. We describe the optical design of an instrument that measures the phasing errors (i.e., tip, tilt, and piston) between two segments under daylight conditions. Its design is based on a high-aperture white-light Michelson interferometer. It was developed at the Center for Sensors, Instruments and Systems Development (CD6) of the Technical University of Catalunya, Spain, and its final testing was carried out on the Gran Telescopio Canarias test workbench.

Background:The purpose of the present study was to investigate two potential sources of variability of the traditional van Herick technique for temporal anterior chamber angle estimation, namely the need to compare the depth of the peripheral anterior chamber (PACD) with the thickness of the peripheral cornea (PCT), and the possible loss of information resulting from restricting the assessment of the anterior chamber angle (ACA) to the temporal limbus. Methods: Both image analysis and Scheimpflug photography were employed to measure PCT and PACD in a group of 82 eyes (mean ± SD age of 32.8 ± 4.1 years) with and without narrow anterior chamber angles. Subjective and semi-objective van Herick grades were compared and the relationship between PCT and PACD was investigated. Scheimpflug photography was also used to determine the value of the narrowest anterior chamber angle and to compare it with the temporal angle. Results: No statistically significant differences were encountered between semi-objective and subjective grades. A weak statistically significant correlation was found between image analysis values for PCT and PACD (r = 0.295; p = 0.007). Upon examining Scheimpflug photographic data, no statistically significant association between PCT and PACD was revealed. Temporal and minimum anterior chamber angles presented statistically significant differences (t = 7.213; p < 0.001). In approximately 65 per cent of the patients, the minimum ACA was not located at the temporal limbus, with a difference of up to 9.8 degrees between minimum and temporal angles. Conclusion:The encountered association between the image analyses of PCT and PACD advocates for the direct measurement of PACD as a better estimation of ACA depth than the ratio between PCT and PACD. All anterior chamber quadrants should be examined, as the minimum ACA may not be located temporally.

We present a simple method for increasing the number of data points obtained during performance of profilometric measurements with the Ronchi test. The method is based on multiple ronchigram acquisitions that are superimposed after a few very simple data-processing operations. The measurement method, experimental setup, and data processing are described in detail from the ronchigram to the measured profile, and experimental results for a concave surface of an spherical ophthalmic lens are provided. The radius of curvature values measured for that surface are compared with the ones obtained with a high-precision radioscope, showing very good agreement and demonstrating the capability of the technique to measure topographic profiles of reflective samples.

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A construction method to obtain sets of tailored facets to be used as the initial configuration in the design of freeform reflector surfaces is presented. The construction strategy starts from a collection of flat elementary facets and achieves the initial configuration of the reflector surface by tailoring the facets according to their Bézier surfaces description. The aim of this research is to describe a procedure capable of generating the Bézier surfaces that define elementary tailored facets; these facets could then be used as initial configurations in the design of freeform reflectors. Though beyond the scope of this article, the facets could be used on a subsequent optimization process, i.e., the geometry of the elementary facets could be modified through a global optimization process taking into account all facets, in order to further improve the entire illumination system. Ray tracing is used to calculate the facet's geometry; it applies elementary merit functions to find the parameters defining the Bézier curve that best meets specifications in each elementary facet. This method is based on a sequential 2D projection strategy that employs different strategic planes for calculations. A method to build up the facet's geometry using a Bézier surface from 2D curves is provided. This approach will successfully generate a net of control points to describe a Bézier surface compatible with any standard optical optimization tool and suitable for use with CAD and other tools that represent solids.