Exact ray-trace beam for an off-axis paraboloid surface

Abstract

When an off-axis paraboloidal mirror focuses a parallel beam, the image is formed on one side of the optical axis. For a tilted beam focused by an off-axis paraboloidal mirror, the focus is no longer pointlike (not considering the diffraction effect); rather, it is a distorted spot. This is due to the inherent aberrations of the surface. In addition, there is a change in the focus position. We calculate by exact ray-trace equations the modified wave-front aberration and express it in power series. Our formulation uses the optical path variation along a defined principal ray that we relate to the parameter that describe the surface and the beam angle of incidence. We designate this ray as that reflected by the center of the entrance pupil and field of view. We employ the direction cosines of the principal ray to compute the wave-front aberration function of a beam reflected by an off-axis paraboloid.

High-speed multiview imaging approaching 4pi steradians using conic section mirrors: theoretical and practical considerations

“…Here, as described in the preceding sections, we are essentially using misalignment to perform lateral scanning. Extending previous studies on characterizing the effects of such aberrations in misaligned parabolic mirrors on focus quality [34][35][36][37][38], here we provide a thorough investigation of the dependence of the lateral FOV, FOV x (or FOV y , which is approximately the same), on a variety of relevant system design parameters: lateral resolution (𝛿 x or 𝛿 y ) or NA, wavelength (𝜆), mirror size (via 𝑓 , or 𝑎 and 𝑏), entry position or sample incidence angle, and telecentric vs. nontelecentric designs. Unless otherwise noted, our results for FOV x and 𝛿 x also apply identically to FOV y and 𝛿 y , respectively.…”

“…To this end, building upon previous works that study the effects of input illumination tilt on focus quality [34][35][36][37][38], we carefully characterize the achievable lateral and axial FOVs over which near-diffraction-limited performance is achievable as a function of various experimental parameters (key equations: Eqs. 24 and 27), such as NA, mirror parameters (e.g., focal length, major and minor axes), sample-incident angle, wavelength, and chief ray geometry (i.e., whether a telecentric design is used).…”

A Modified 8f Geometry with Reduced Optical Aberrations for Improved Time Domain Terahertz Spectroscopy

“…In the present work, we show that reduced focal spot sizes can also be achieved via a particular arrangement of the off axis parabolic mirrors (OAPs) typically used to direct and focus THz radiation. We demonstrate, through simulations and data, that our proposed modified mirror geometry significantly reduces optical aberrations, which stem from finite sized source effects [27,28], resulting in a substantial reduction in the THz focal spot size and thus easing the requirement of large sample sizes in TDTS spectroscopy. …”

A Space-Variant Deblur Method for Focal-Plane Microwave Imaging

“…For parabolic reflectors, the characteristics of off-axis and non-parallel incident rays cause relatively large aberrations. In the literature [22,23], Arguijo used the ray tracing method in geometric optics to analyze the aberration of the off-axis parabolic reflection mirror in optical imaging systems, pointing out that the aberration mainly includes astigmatism and coma. According to Seidel's primary aberration theory, the astigmatism and coma can be described by polar-coordinates as follows [12,24]:…”