Optical aspherical surfaces have become more widely used as they offer advantages such as improved image quality, compact design, increased light gathering, and reduced distortion. However, measuring aspherical surfaces presents challenges due to their non-spherical shapes. The primary difficulties include the complexity of surface geometries and the need for specialized metrology equipment. These challenges require advanced measurement techniques to ensure accurate characterization and quality control of aspherical surfaces in various applications. This paper introduces an innovative, AI-driven solution for the measurement of aspherical surfaces within the image space, offering a flexible optical metrology tool for measuring aspherical surfaces. This approach is characterized by its ability to deliver rapid and cost-effective integration without the need for custom, complex optics.
The use of artificial intelligence (AI) software for wavefront sensing has been demonstrated in previous studies. In this work, we have developed a novel approach to wavefront sensing by coupling an AI software with an Autostigmatic Microscope (AM). The resulting system offers optical component and system testing capabilities similar to those of an interferometer used in double pass, but with several advantages. The AM is smaller, lighter, and less expensive than commercially available interferometers, while the AI software is capable of reading out Zernike coefficients, providing real-time feedback for alignment. Our AI software uses an artificial neural network (NN) that is trained to output the Zernike coefficients, or any other relevant figures of merit, exclusively from synthetic data. The synthetic data includes random Zernike coefficients for a parametric description of the wavefront, noise, and a defocus error to avoid any stringent accuracy requirement. Once trained, the NN yields Zernike coefficients from a single frame of defocused intensity. The feedforward architecture of the NN enables swift output of Zernike coefficients, eliminating the need for iteration or optimization during run time. Using the software with an AM allows for paraxial alignment of the object in the test cavity, with the real-time Zernike coefficients guiding the item into optimal alignment. This double pass test is not possible with most other types of wavefront sensors, as they are designed for single-pass use. Our results demonstrate that the test results obtained compare well with modeled results, and that errors in the AM can be removed by calibration, as in the case of interferometer transmission spheres. Furthermore, the simple defocused image of a source provides non-ambiguous phase retrieval, which competes with traditional wavefront sensors such as Shack-Hartmann (SH) sensors or interferometers. The AI software provides high dynamic range, sensitivity and precision. This novel approach to wavefront sensing has significant potential for use in a wide range of applications in the field of optics.
We describe a new, simple wavefront sensing method that uses a single measurement of a defocused star and a neural network to determine low-order wavefront components. The neural net is trained on computed diffracted star image data at 640 nm to output annular Zernike terms for an obscured circular aperture over a discrete range of all values. In the context of an actual star, the neural-net also provides the Fried’s parameter as an estimation of atmospheric turbulence. It is shown that the neural-net can produce a robust, high accuracy solution of the wavefront based on a single measurement. The method can also be used to simultaneously determine both on-axis and fielddependent wavefront performance from a single measurement of stars throughout the field. The prototype system can run at a rate of about 1 Hz with Python interpreted code, but higher speeds, up to video rates, are possible with compilation, proper hardware and optimization. This technique is particularly useful for low-order active-optics control and for optical alignment. A key advantage of this new method is that it only requires a single camera making it a simple cost-effective solution that can take advantage of an existing camera that may already be in an optical system. Results for this method are compared to high-precision interferometric data taken with a 4D Technology, PhaseCam interferometer and with an Innovations Foresight StarWave Shack Hartmann sensor from ALCOR SYSTEM under well-controlled conditions to validate performance. We also look at how the system has been implemented to use starlight for aligning multiple mirror telescopes in the presence of atmospheric seeing.
We present a low-cost stand-alone AI based wavefront sensor (AIWFS) trained only with synthetic data. A simple defocused image of a source provides non-ambiguous phase retrieval competing with traditional wavefront sensors such a Shack-Hartmann (SH) sensor. An artificial neural network (ANN) is trained to output the Zernike coefficients, or any other relevant figures of merit, exclusively from synthetic data. The synthetic data typically contains random Zernike coefficients or wavefront, noise, as well as a defocus error to avoid any stringent accuracy requirement. Once trained, the AIWFS can be used directly on many other applications without any retraining. In its simplest form, the AIFWS’s hardware is just a camera taking defocused images of a point source, like a star. However, with the proper synthetic data, many types of source and optical layouts can be accommodated, such multi-point, or extended, sources to simultaneously determine both on-axis and field-dependent wavefront performance, from a single measurement. In applications using actual stars, the NN also provides the Fried’s parameter as an estimation of atmospheric turbulence. The ANN outputs are computed directly there is no numerical iteration nor any convergence consideration. The system can run at video rates, in real time, and therefore is suitable for analyzing systems with vibrations or moving parts. The AIWFS only requires a single camera making it a simple cost-effective solution that can take advantage of an existing camera that may already be in an optical system. This paper shows results using AIFWS for telescopes with both actual and artificial stars.
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