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For a spherical mirror the principal focus (F) lies exactly mid-way between the pole (P) and centre of curvature (C). So, the focal length (f) of a spherical mirror is equal to half of its radius of curvature (R).

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Spherical aberrationand chromaticaberration

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All necessary code and instructions for running the axial correction macro are provided in the Supplementary Software and Box 1.

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What is a spherical aberrationclass 12

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Spherical aberration (SA) occurs when light rays entering at different points of a spherical lens are not focused to the same point of the optical axis. SA that occurs inside the lens elements of a fluorescence microscope is well understood and corrected for. However, SA is also induced when light passes through an interface of refractive index (RI)-mismatched substances (i.e., a discrepancy between the RI of the immersion medium and the RI of the sample). SA due to RI mismatches has many deleterious effects on imaging. Perhaps most important for 3D imaging is that the distance the image plane moves in a sample is not equivalent to the distance traveled by an objective (or stage) during z-stack acquisition. This non-uniform translation along the z axis gives rise to artifactually elongated images (if the objective is immersed in a medium with a higher RI than that of the sample) or compressed images (if the objective is immersed in a medium with a lower RI than that of the sample) and alters the optimal axial sampling rate. In this tutorial, we describe why this distortion occurs, how it impacts quantitative measurements and axial resolution, and what can be done to avoid SA and thereby prevent distorted images. In addition, this tutorial aims to better inform researchers of how to correct RI mismatch–induced axial distortions and provides a practical ImageJ/Fiji-based tool to reduce the prevalence of volumetric measurement errors and lost axial resolution.

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What is spherical aberrationand How can it be corrected

Peer review information Nature Protocols thanks Chrysanthe Preza and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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We thank S. Piccinotti and L. Rubin for providing organoid samples. We thank the Harvard Center for Biological Imaging for infrastructure and support. J.W.L. was supported by the following funding sources: National Institutes of Health grants P50 MH094271, U24 NS109102, and U19 NS104653 and Department of Defense MURI award GG008784.

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The idea for calculating axial distortion correction factors as described in this tutorial was conceived by D.S.R. and J.W.L. E.E.D. and D.S.R. carried out experiments and analyzed data. D.S.R., J.W.L. and E.E.D. wrote the manuscript. All authors contributed to editing the final manuscript.

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The distance from the pole to the focal point is called the focal length (f). The relationship between the focal length f and radius of curvature R is R = 2f. For a spherical mirror the principal focus (F) lies exactly mid-way between the pole (P) and centre of curvature (C). So, the focal length (f) of a spherical mirror is equal to half of its radius of curvature (R).For a spherical mirror (both for a concave and for convex), the focal length is half of radius of curvature.

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