Deflectometry is a metrology method able to measure large surface slope ranges that can achieve surface reconstruction accuracy similar to interferometry, making it ideal for freeform metrology. While it is a non-null method, deflectometry previously required a precise model of the unit under test to accurately reconstruct the surface. However, there are times when no such model exists, such as during the grinding phase of an optic. We developed a model-free iterative data processing technique which provides improved deflectometry surface reconstruction of optics when the correct surface model is unknown. The new method iteratively reconstructs the optical surface, leading to a reduction in error in the final reconstructed surface. Software simulations measuring the theoretical performance limitations of the model-free processing technique as well as a real-world test characterizing actual performance were performed. The method was implemented in a deflectometry system and a highly freeform surface was measured and reconstructed using both the iterative technique and a traditional non-iterative technique. The results were compared to a commercial interferometric measurement of the optic. The reconstructed surface departure from interferometric results was reduced from 44.39 μm RMS with traditional non-iterative deflectometry down to 5.20 μm RMS with the model-free technique reported.
We present an instantaneous phase mapping deflectometry (PMD) system in the context of measuring a continuous surface deformable mirror (DM). Deflectometry has a high dynamic range, enabling the full range of surfaces generated by the DM to be measured. The recent development of an instantaneous PMD system leverages the simple setup of the PMD system to measure dynamic objects with accuracy similar to an interferometer. To demonstrate the capabilities of this technology, we perform a linearity measurement of the actuator motion in a continuous surface DM, which is critical for closed loop control in adaptive optics applications. We measure the entire set of actuators across the DM as they traverse their full range of motion with a Shack-Hartman wavefront sensor, thereby obtaining the influence function. Given the influence function of each actuator, the DM can produce specific Zernike terms on its surface. We then measure the linearity of the Zernike modes available in the DM software using the instantaneous PMD system. By obtaining the relationship between modes, we can more accurately generate surface profiles composed of Zernike terms. This ability is useful for other dynamic freeform metrology applications that utilize the DM as a null component.
A segmented mirror is one of the most promising solutions to build an extremely large aperture telescope to reveal the secrets of the universe. In this manuscript, we present a simultaneous angle alignment method for segmented mirrors. By taking the displayed sinusoidal pattern reflecting off the mirrors, the tip-tilt angles are measured with 0.8 μrad resolution for a flat mirror. Due to the efficient calculation using Fourier analysis, the total measurement time for seven flat mirrors is 0.07 s. In addition, a multiplexed sinusoidal pattern is adapted to resolve the intrinsic 2π ambiguity problem in a sinusoidal signal. The presented method can measure any number of segmented mirrors provided that the camera’s field of view can cover them all simultaneously.
Dynamic metrology holds the key to overcoming several challenging limitations of conventional optical metrology, especially with regards to precision freeform optical elements. We present two dynamic metrology systems: 1) adaptive interferometric null testing; and 2) instantaneous phase shifting deflectometry, along with an overview of a gradient data processing and surface reconstruction technique. The adaptive null testing method, utilizing a deformable mirror, adopts a stochastic parallel gradient descent search algorithm in order to dynamically create a null testing condition for unknown freeform optics. The single-shot deflectometry system implemented on an iPhone uses a multiplexed display pattern to enable dynamic measurements of time-varying optical components or optics in vibration. Experimental data, measurement accuracy / precision, and data processing algorithms are discussed.