This work describes a process for measuring thin film steps, using phase shifting interferometry (PSI). The phase shifts are applied only in the region where the thin film steps are located. The phase shift is achieved by displaying different gray levels on a spatial light modulator (SLM Holoeye LC2012) placed in one arm of a Twyman–Green (T–G) interferometer. Before measuring the thin film steps, it was necessary to quantify the phase shifts achieved with this SLM by measuring the fringe shifts in experimental interferograms. The phase shifts observed in the interference patterns were produced by displaying the different gray levels on the SLM one by one, from 0 to 255. The experimental interferograms and the thicknesses of the thin film steps were successfully quantified, proving that this method can be used to measure thin films by applying the PSI method only on the region occupied by them.

A new alternative to calculate the null-screen for highly freeform or complex surfaces for any desired pattern to be observed on the detector is presented. To validate the proposed method, we used the Zernike polynomials to design complex surfaces with sagittas greater or equal to 40 mm, and peak to valley greater or equal to 30 mm, between the used surface and the best fit sphere. The freeform surfaces were fabricated using a 3D printer and a five-axis CNC machine. With the proposed method we can calculate the image that will be observed over the detector for any null-screen and any freeform surface that want to be analyzed. The results showed that the proposal works very well for extremely fast complex freeform surfaces (with slopes ≤ 80°), obtaining an error smaller than 0.66% in PV and 0.36% in rms in sagitta differences.

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.

A method for the evaluation of the shape of fast conical surfaces based on the null-screen method is presented. The proposed method is based on randomized algorithms, where instead of integration as is usually performed, the shape of the surface is recovered in a direct and random way. This is done by proposing a new test surface; the surface parameters are randomly generated and the calculated null-screen is compared against the originally designed one. The coefficients that generate the null-screen closest to the reference null-screen are taken as the final values that describe the surface under test. The algorithm validation was done in the theoretical and experimental way. For the theoretical way, a convex parabolic surface with 21.36 mm radius of curvature and f/0.178 was simulated and analyzed; in the experimental way, a convex spherical surface f/0.33 and a concave ellipsoidal mirror f/0.2381 were evaluated. The results obtained with our algorithm in the evaluation of the ellipsoidal surface were compared against the results obtained with traditional methods. We found that the radius of curvature, conic constant, and the decentering coefficients that were used to generate each surface were retrieved in a good manner with our algorithm. The results show that these parameters can be recovered with a percent error smaller than 1% in the case of simulations, and smaller than 2% in the two experimental cases.

In this work, we present the methods of fabrication and characterization of biconvex spherical and aspherical lenses with 25 and 50 mm diameters that have been created via additive technology using a Formlabs Form 3 stereolithography 3D printer. After the prototypes are postprocessed, fabrication errors ≤ 2.47 % for the radius of curvature, the optical power, and the focal length are obtained. We show eye fundus images captured with an indirect ophthalmoscope using the printed biconvex aspherical prototypes, proving the functionality of both the fabricated lenses and the proposed method, which is fast and low-cost.

Misalignments are a common problem in corneal topography reconstruction. To determine the topography of the surface using a corneal topographer based on the null-screen method, it is necessary to measure errors caused by mechanical misalignment of the topographer, which could influence the results of this technique but are not related to the quality of the corneal surface. To evaluate the variability in measurements, in this work, we simulate some misalignments in the optical system, for the simulation we design a semi-radial null-screen to test a reference spherical surface to identify the variations in results introduced by misalignment errors of the corneal topographer with respect to the test surface. According to the simulations, the accuracy of the null-screen method ranges from 0.81 µm to 2.84 µm for typical tilt, decentering, and defocusing errors. Experimental results for the testing of a spherical surface are shown. After removing the misalignments, we found that the variations are approximately 3.5 μm rms value measured with respect to the best-fitting sphere, and the radius of curvature differs approximately 0.06% from the design value.