Published Papers

We use a known optic, a catalog off-axis parabola, as a reference to both model in Zemax and to align while tracking the position of the focus in 3 degrees of freedom (DOF) and the tilt of the auto-reflecting flat in 2 DOF to demonstrate a systematic approach to alignment. The aberrations present at each step of the experimental procedure are monitored using an autostigmatic microscope.

In this study, we explore the behavior of Bessel beams as they propagate through a misaligned apertured optical system in practice. Based on experimental observations, we propose what we believe to be a novel hypothesis that a Bessel beam propagating through an optical system behaves identically to a paraxial ray under certain conditions. We then derive analytical formulas for the propagation of Bessel beams in Cartesian coordinates and the Huygens-Fresnel principle. Additionally, another simulation employing Gaussian decomposition was conducted, and we compared both simulations with experimental results, demonstrating a high correlation. Our findings indicate that Bessel beams can be interpreted as meridional rays when passing through misaligned spherical surface systems, allowing us to achieve quasi-ray tracing in practice. We further discuss the significance of utilizing this property of Bessel beams for precise optical alignment, highlighting its potential to enhance the accuracy and efficiency of optical systems.

Following the discovery of so called non-diffracting Bessel beams [1], they have been used for a number of exotic purposes such as trapping single atoms and aiding in the discovery of exoplanets. We discuss more mundane but practical methods applicable to precision engineering, and the physical ray tracing of a ball lens in transmission to determine if it behaves as geometrical optics predicts.

The article demonstrates a new approach for achieving high-accuracy alignment with a Bessel-Gauss Beam by utilizing its property of propagating as a paraxial ray. © 2024 OSJ

In this paper we step back from complex CGH patterns used to test aspheric and freeform optics to ask what can be done with the simplest CGH patterns and the high precision of pattern location on a photomask substrate4. We first describe the use of patterns of equally spaced concentric circles to create an axis in space perpendicular to the CGH plane, and the Fresnel zone patterns that produce points in space when illuminated with a point source of light.

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.

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.

Bessel beams have found use in the alignment of transmissive optics for some time. They are also used for the alignment of reflecting optics when used in the imaging mode, that is, when the wavefront is near spherical. However, there are cases where it would be useful to use the Bessel beam for alignment of far-off axis aspheres to order to get the asphere aligned close enough to its final position that light will go through the system in the imaging mode. In another mode, the Bessel beam is used to determine the normal to a free form surface.

The use of artificial intelligence (AI) software for wavefront sensing has been demonstrated in previous studies [1], [3]. 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.

The Point Source Microscope (PSM) is used to find five aberrations related to the symmetries of the autostigmatic image viewed when aligning aspheric mirrors to a point along an axis. These five aberrations exactly match in number the five degrees of mechanical freedom required to align the mirror to an axis and thus provide an exact solution to a unique focus and alignment to an axis. We show how the PSM is used to capture and analyze a set of images as the PSM is moved through focus using the symmetry properties of the image.

We present a description of an attachment for an autostigmatic microscope that uses two objectives set at right angles to unambiguously locate the center of a ball in all 3 translational degrees of freedom that can be used to perform the “R” test, or to scan a ball plate, to determine machine tool precision dynamically.

We show how custom computer generated holograms (CGH) are used along with an autostigmatic microscope (ASM) to align both optical and mechanical components relative to the CGH. The patterns in the CGHs define points and lines in space when interrogated with the focus of the ASM. Once the ASM is aligned to the CGH, an optical or mechanical component such as a lens, a well-polished ball or a cylinder can be aligned to the ASM in 3 or 4 degrees of freedom and thus to the CGH. In this case we show how a CGH is used to make a fixture for cementing a doublet lens without the need for a rotary table or a precision vertical stage.

A novel method of projecting a reference axis in space for use in optical assembly of centered elements such as assembly in a barrel or in cementing multi-element lenses is presented. An axicon grating, a set of concentric, uniformly spaced circles, when illuminated with a point source of light creates a line of bright spots surrounded by concentric rings in both transmission through and reflection from the grating. This axis is easily interrogated with an autostigmatic microscope to gauge the distance a center of curvature, or other lens conjugate, lies from the axis created by the grating.

An optical method of determining the location of the apex of a corner reflector mounted in a steel ball, commonly referred to as a Spherically Mounted Retroreflector (SMR), relative to the center of the ball to the 1-2 μm level was previously described by us. The method used an autostigmatic microscope focused on the apex and viewed the reflected spot image as the SMR was rotated about a normal to its entrance aperture. This measurement determined the lateral offset of the apex and tipping the SMR while viewing the spot gave an indication of the axial displacement.

Axicon gratings are computer generated holograms of equally spaced concentric circles printed on a plane substrate. When illuminated by a point source of light they create axes in space defined by a line between the point source and the center of the grating pattern. The axis can be viewed in either transmission or reflection with an autostigmatic microscope. The axis created by the grating can be located to less than 1 um in translation and depending on distance from the grating to less than 1 microradian in angle. Several examples of such a use in alignment are explained.

The positioning accuracy of multi-axis machine tools and coordinate measuring machines are often checked using ball bars or ball plates where the spatial locations of the balls are externally calibrated to provide a traceable artifact [1,2]. In use, the individual ball surfaces are probed in at least 4 places with a tactile sensor and the points of contact fit to the equation of a sphere to determine the center of the ball. The method is tedious, indirect and semi-static. Furthermore, it is difficult or impossible to create artifacts that truly span the three-dimensional work volume of machines because some features become occluded by others and cannot be accessed.

Measuring the quality of alignment of an assembled compound lens is often necessary. This raises the question of what axis to use as a reference axis for this measurement. We suggest that the reference axis should be the optical axis of the assembled system and that this axis is unique for each assembly.

INTRO: INTRODUCTION Almost all optical elements and systems are sym- metric about their optical axes which means there are only 5 degrees of freedom that will affect op- tical alignment. Likewise, stigmatic images of a point source of light imaged by a finite conjugate optical system have 5 types of symmetry. There is a part of the image that is symmetric about the centroid of the image, and there are 4 symmetries in the plane of the image, namely, even-even, odd-odd, even-odd and odd-even. We show there is a one-to-one correspondence between the im- age symmetries and the degrees of freedom op- tical elements can be moved to align them.