We report the testing of a fast off-axis surface based on the null screen principles. Here we design a tilted null screen with drop shaped spots drawn on it in such a way that its image, which is formed by reflection on the test surface, becomes an exact square array of circular spots if the surface is perfect. Any departure from this geometry is indicative of defects on the surface. Here the whole surface is tested at once. The test surface has a radius of curvature of $r=20.4\mathrm{mm}$ ($F/0.206$). The surface departures from the best surface fit are shown; in addition, we show that the errors in the surface shape are below $0.4\mathrm{\mu m}$ when the errors in the determination of the coordinates of the centroids of the reflected images are less than 1 pixel, and the errors in the coordinates of the spots of the null screen are less than $0.5\mathrm{mm}$.

In order to measure the shape of fast convex aspherics, such as the corneal surface of the human eye, we propose the design of a conical null-screen with a radial point distribution (spots similar to ellipses) drawn on it in such a way that its image, which is formed by reflection on the test surface, becomes an exact array of circular spots if the surface is perfect. Any departure from this geometry is indicative of defects on the evaluated surface. We present the target array design and the surface evaluation algorithm. The precision of the test is increased by performing an iterative process to calculate the surface normals, reducing the numerical errors during the integration. We show the applicability of the null-screen based topographer by testing a spherical calibration surface of 7.8 mm radius of curvature and 11 mm in diameter. Here we obtain an rms difference in sagitta between the evaluated surface and the best-fitting sphere less than 1 μm.

The blades in a wind turbine are currently manufactured with flexible and light materials, which make them more susceptible to the effects of vibrations when the wind speed is high enough, causing fatigue damage, affecting the functionality of its structure and aerodynamic efficiency. This work presents a comparison of the modal vibration parameters, applied to a cantilever beam, determined with two experimental methods—the use of accelerometers and a proposed optical non-contact method—based on the principle of laser triangulation and photogrammetry techniques. This technique uses the geometric symmetry of the equidistant displacements along the z axis of the beam to obtain the amplitude data. Parameters such as natural frequency and modal form are obtained by fitting the data to a nonlinear equation with a solution which is an exponential/harmonic equation. Also, analytically, these parameters are determined, and a comparison is made between the experimental methods. The result shows that the relative error of the first-order natural vibration frequency is below 1%. The proposed method is simple, efficient, reliable, and it is also a method that has not been applied to the test of wind turbine blades, so its implementation as this type of wind turbine component is an area of opportunity for the validation of modal vibration parameters in the wind industry. An analysis of results is presented showing benefits of the proposed method and its limitations.

In this work, we present a technique for quantitatively assessing the optical quality of a parabolic trough solar collector. The presented method is an adaptation of the null-screen technology, a collection of processes that retrieve information from the reflection of a known object from the surface and then use that information to reconstruct the surface’s normal vectors. Via numerical simulations, it is shown that the precision attainable by this method is up to 0.068 mrad, depending on the source of systematical error. In this study we only consider displacements of the physical null-screen as sources of error.

A method for increasing the precision and sensitivity of the quantitative evaluation of fast aspheric surfaces through the null screen method is presented. This consists of applying small displacements to the cylindrical null screen along the optical axis. These movements allow a scan of the image spots over zones that with the analysis of a single image are more difficult to evaluate. The precision of the test is increased due to a greater density of sampling reducing the numerical errors during the integration. Results of the evaluation of an elliptical concave mirror on axis show that the numerical integration errors can be reduced from 20% for short paths to 80% for larger integration paths.

To measure the shape of the fast corneal surface of the human eye, we propose the design and characterization of a compact corneal topographer using the capabilities of a smartphone. The performance evaluation of the compact corneal topographer includes the calculation and compensation of the distortion introduced by the smartphone lens used to acquire the images and the evaluation of a reference surface. To demonstrate the feasibility of our proposal, we performed surface topography measurements on some human corneas and compared the results with those obtained by a commercial corneal topographer. We showed that the results obtained with our algorithms were consistent with other methods that analyze the corneal surface.