Exact equations to measure highly aberrated wavefronts with the Hartmann test

Method for testing freeform surfaces based on a Shack-Hartmann sensor with plane wavefront scanning and stitching

Currently, the surface error measurement technology for freeform faces a significant contradiction between measurement accuracy and dynamic range. The study proposes a non-null testing method for measuring freeform surfaces by utilizing a Shack-Hartmann wavefront sensor to emit a small aperture parallel beam and scan along the normal direction at the center of subapertures for stitching (SHPSS). A mathematical model based on ray tracing and the reflection theorem is established to calculate the sampling points on an ideal freeform surface, the reference spot array on CCD, and the corresponding relationship between microlens array and spots. An algorithm is proposed to iteratively calculate the wavefront aberration and gradually approach the actual sampling points using the established model. Theoretical analysis and numerical simulation results indicate that SHPSS can increase the dynamic range and improve the accuracy of wavefront reconstruction. The error analysis of the SHPSS method is carried out, the measurement accuracy of full aperture freeform surface is 11.45 nm. A testing system is set up and experiments are conducted on a 100 mm aperture freeform reflective mirror. The RMS of the SHPSS test results is less than λ/30 (λ=635 nm) compared to the interferometric test results. By analyzing five groups of repeated measurement experiments, the repeatability accuracy of SHPSS method is less than 1/80 λ (RMS). This demonstrates the feasibility and measurement capabilities of the method for freeform surface testing.

Exact formula to relate optical path differences and transversal aberration components

An exact equation to relate the optical path differences (OPD) with its transversal aberration components (TAC) is determined. The OPD-TAC equation reproduces the Rayces formula and introduces the coefficient for the longitudinal aberration. The defocus orthonormal Zernike polynomial (Z _DF) is not a solution for the OPD-TAC equation since the obtained longitudinal defocus depends on the ray height on the exit pupil, meaning that it cannot be interpreted as a defocus. In order to find an exact expression for OPD defocus, first, a general relationship between the wavefront shape and its OPD is established. Second, an exact formula for the defocus OPD is established. Finally, it is proved that only the exact defocus OPD is an exact solution of the exact OPD-TAC equation.

Inverse Hartmann test for radius of curvature measurement in a corneal topography calibration sphere

In this article, the use of a square Hartmann screen test to measure the radius of curvature of a corneal topography calibration test sphere is presented. The proposed technique is based on the image formation principle by specular reflection on convex reflective surfaces. Applying an inverse Hartmann test, a de-magnified virtual image (Hartmanngram) is obtained; considering their own scaled reference screen plate, a zonal wavefront retrieval approach is used and the radius of curvature obtained. Experimental setup along the obtained results is presented. A simulated spherical wavefront is used as a method to evaluate the error in the wavefront reconstruction. Since the measurements of radius of curvature fits in to ISO 10343, through suitable modifications the proposed method is potentially applicable in small F/# convex specular surfaces, as is the case in keratometry and corneal topography measurements.

Freeform gradient index progressive addition lens raytrace performance evaluation

Raytrace evaluation capable of evaluating progressive addition lens (PAL) designs with freeform surface and gradient index (GRIN) contributions is presented. The method is validated on an analytically generated PAL start design and on optimized surface designs. Surface raytrace evaluations are compared with the surface-geometric evaluation commonly presented for freeform surface PAL designs. The evaluation is also tested on analytically generated freeform GRIN PAL designs with spherical and plano surfaces. The raytrace method agrees with the analytic performance and surface-geometric performance near the center of the lens and deviates at the edge of the lens, due to ray obliquity with the surfaces and aggregate contributions of surfaces and/or GRIN. These deviations are expected, as the raytrace model accounts for more physical contributions to optical performance, including pupil diameter and eye position. This raytrace method enables the evaluation of lens performance contributions other than from polished surfaces on homogeneous materials, enabling further exploration of GRIN in PAL designs.

Null screens to evaluate the shape of freeform surfaces: progressive addition lenses

We propose a method for measuring the shape of freeform surfaces such as Progressive Addition Lenses (PAL). It is based on optical deflectometry by considering a non-uniform pattern of spots computed by using the null-screen method. This pattern is displayed on a flat LCD monitor being reflected on the freeform under test and whose image is recorded on a CCD camera placed at a predefined off-axis position. We use one image to calibrate the experimental setup and another to measure the freeform surface. We develop an iterative algorithm to retrieve the surface under test and calculate the spherical and cylindrical dioptric powers of the frontal freeform of a commercial PAL under test.