Spherical aberration

Spherical aberration (SA) is an optical effect occurring when the oblique light rays entering a lens are focused in a different plane than the central rays. The result is that rays coming from the same light source (or same object in the sample) are out of focus relative to each other, causing blurring of the object in the image plane.

To the right you see an example of spherical aberration in an image due to a mismatch in refractive indices. This example is explored in more detail at the bottom of this page. Spherical aberration is a common issue in microscopy that is especially hard to correct for images with a large Z-range. Luckily the unique spherical aberration in Huygens can correct for this easily.

Figure description: MIP projections along the XZ axis of 3D Drosophila brain images, without post-acquisiton processing (original, left), Huygens deconvolved without spherical aberration correction (middle) and Huygens deconvolved with spherical aberration correction (right). Courtesy of Tory Herman, Institute of Molecular Biology, University of Oregon, Eugene, Oregon, USA

Spherical aberration in microscopy

Two forms of spherical aberration are relevant in light microscopy. The most described form is SA due to the lens shape. The other form is SA due to a mismatch in refractive indices between sample and the lens immersion medium. To learn more about refraction and refractive indices, please read our refractive indices page.

Lens spherical aberration

Spherical aberration occurs in all lens-based systems due to the spherical shape of the lens. Light entering near the edges is refracted more strongly than light near the optical axis, causing rays from the same source to focus at different planes. This results in a sharp center but blurry edges. However, modern microscopes typically include corrective elements to minimize this effect.

Figure description: ZX (optical axis horizontal) slice of a lens with spherical aberration. Light rays towards the lens edges are bend more strongly and are thus focussed in different points compared to central rays. Dotted vertical line represent the image plane.

Refractive index mismatch

In widefield and confocal microscopy, spherical aberration mainly arises from mismatched refractive index (RI) between the lens immersion medium and the sample embedding medium. This mismatch causes light to refract differently depending on the angle of incidence (light refraction), leading rays from a single point to focus at different planes. The focal shift increases with the depth of focus in the sample.

Figure description: ZX (optical axis horizontal) of spherical aberration by a lens due to a refractive index (RI) mismatch. Red rays show refraction at the interface between the media, gray dotted rays represent rays in case of no mismatch between refractive indices. Dotted vertical line represents the image plane, solid vertical line represents a confocal pinhole, showing how spherical aberration causes loss of light from the same point source.

Correcting spherical aberration with Huygens deconvolution

Spherical aberration due to refractive index mismatches can be automatically corrected for by performing Huygens deconvolution. Spherical aberration is automatically corrected for if the following two conditions are met:

Setting coverslip position in Huygens

If your image suffers from a Refractive Index mismatch, make sure to check that the imaging direction and coverslip position are set as they were during acquisition of the image in the microscopy parameters before doing deconvolution. If you are not sure what the orientation of your dataset is, you can always guess it from the asymmetry of the PSF of the cones of light. In the image above showing the PSF distortion, the smooth side of the PSF (bottom of the image) is at the side of the coverslip. For more information see also Point-Spread-Function.

Avoid SA correction in Huygens

To switch the SA correction off (because despite the refractive index mismatch you have other physical correctors in your setup) just set the image Microscopic Parameters to have matching lens refractive index and Medium Refractive Index prior to Deconvolution. If the Numerical Aperture is larger than either of the refractive indices, make sure you use set both RIs to the lowest RI, to allow the software to correctly account for total internal reflection.

Air lenses

Air lenses require special consideration: they may be corrected for spherical aberration and they may behave as, e.g., glycerine lenses, and therefore you will not expect problems if you use glycerol as embedding medium. You can then think about deactivating the SA correction as explained in the previous paragraph. However, this only seems to work well for imaging close to the coverslip. Deeper imaging positions still benefit greatly from the spherical aberration correction by Huygens. Read more in Air Lens Correction for considerations when using air lenses.

RI mismatch distorts PSF

Spherical aberration due to a RI mismatch has strong effects on the PSF shape. In particular, when imaging thick samples, the PSF is stretched out and appears more blurred in deeper layers. If the mismatch is large, e.g. when going from oil lens immersion medium into a watery sample embedding medium, the Point Spread Function will become asymmetric at depths of already a few micron. In the image on the right you see an example of this deformation.

If this is the case for your image, you can work around it by keeping the Z-range of the data as small as possible and measure only close to the coverslip. To resolve the issue the lens immersion medium can be matched to the RI of the sample embedding medium (RI ~ 1.33).

The PSF distortions due to RI mismatches for different imaging depths are shown in more detail on our Point-Spread-Function page.

Figure description: XZ (optical axis vertical) slice of a Huygens generated PSF using oil (RI ~ 1.51) as lens immersion medium and water (RI ~ 1.33) as the sample embedding medium. Left: depth 0 respective to the coverslip position. Right: depth 30 µm respective to the coverslip position. Increasing depth distorts the PSF and causes asymmetry.

Practical example

To illustrate the effects of a RI mismatch and the resulting spherical aberration, consider the following case study. Here, active zones of synapes in adult Drosophila brains are visualized by endogeneous expression of GFP labeled Bruchpilot (Brp). Data was acquired and provided by Tory Hermans, Institute of Molecular Biology, University of Oregon, Eugene, Oregon, USA.

In this example, the images were obtained using a confocal microscope and using oil (RI = 1.51) as lens immersion medium and Vectashield (RI = 1.45) as the sample embedding medium. Despite the small mismatch you can clearly see the differences in the structures with and without spherical aberration. With SA correction, the structures appear sharper and better distinguishable.

Figure description: Left: Drosophila brain deconvolved with Huygens. Right, same image, but deconvolved with spherical aberration correction.

If we make a XZ MIP projection of sections of these images you can clearly see the effects of the RI mismatch. The raw data (left image) displays elongated structures due to the fishtank effect and RI mismatch induced spherical aberration causes objects to appear blurred and out-of-focus. This blurring is stronger at the top of the image. When deconvolving this image without properly setting the mismatch between the lens refractive index and sample refractive index, the deconvolved result will show similar spherical aberration. When deconvolving with the (proper) values for the refractive indices, depth dependend spherical aberration will be taken into account for deconvolution, thus correcting the problems in the image.

Figure description: MIP projections along the XZ axis of 3D Drosophila brain images, without post-acquisiton processing (original, left), deconvolved without spherical aberration correction (middle) and deconvolved with spherical aberration correction (right).

To see the implications this has for image analysis, the synapses have been studied using the Huygens Object stabilizer. The corrected image has much shorter objects, due to lack of stretching and spehrical aberration widening the objects. The graph also clearly shows that the objects become longer (more stretched) deeper in the sample in the uncorrected image. Moreover, roughly 10% more structures could be segmented in the spherical aberration corrected image because of the resulting contrast and resolution improvement.

Figure description: Left panels: Huygens object analysis of the drosophila brain slices without spherical aberration (SA) correction (top) and with SA correction (bottom). Right graph shows the average length of objects for varying ranges of imaging depth for the corrected image (orange) and the uncorrected image (blue).

Related

Refractive Index Point-Spread-Function Parameter variation

References

Diel, E.E., Lichtman, J.W. & Richardson, D.S. Tutorial: avoiding and correcting sample-induced spherical aberration artifacts in 3D fluorescence microscopy. Nat Protoc 15, 2773–2784 (2020). https://doi.org/10.1038/s41596-020-0360-2

Last updated: June 2024