Abstract
Nodal aberration theory is used to calculate the third-order aberrations that result in image blur for an unobscured modified 4f relay (2f1 + 2f2) formed by two tilted spherical mirrors for objects at infinity (infinite conjugate) and near the front focal plane of the first mirror (finite conjugate). The field-averaged wavefront variance containing only non-rotationally symmetric aberration coefficients is then proposed as an optimization metric. Analytical and ray tracing optimization are demonstrated through sample designs. The particular cases of in-plane and orthogonal folding of the optical axis ray are discussed, followed by an analysis of a modified 2f1 + 2f2 relay in which the distance of the first mirror to the object or pupil is allowed to vary for aberration correction. The sensitivity of the infinite conjugate 2f1 + 2f2 relay to the input marginal ray angle is also examined. Finally, the optimization of multiple conjugate systems through a weighted combination of wavefront variances is proposed.
Highlights
The reflective relay telescope was first reported shortly after the reflective telescope objective in the 17th century, it was not until the late 19th century that it became widely adopted after the invention of film photography, the spectroscope, and the glass mirror [1,2,3]
To analytically study the unobscured reflective relay at both the finite and infinite conjugates, we evaluate this metric accounting for third-order aberrations
When tested in sample reflective 2f1 + 2f2 relays, the optimal angles were in close agreement with those obtained with real ray tracing software
Summary
The reflective relay telescope was first reported shortly after the reflective telescope objective in the 17th century, it was not until the late 19th century that it became widely adopted after the invention of film photography, the spectroscope, and the glass mirror [1,2,3]. Mathematical theories of non-symmetrical systems centered on small perturbations of rotationally symmetric systems [22,23,24], closed-form expressions of ray paths such as the Coddington equations [25], real ray tracing schemes [26,27], and expansion of the imaging properties around a central ray [28,29,30] This last approach has more recently been generalized and demonstrated in a variety of unobscured mirror systems [31,32,33,34,35,36,37]. A natural extension to the optimization method is proposed to deal with multiple conjugates simultaneously
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