### Table of Contents

# Objectives

The choice of light sheet objectives is limited because they must be co-focused without bumping into each other. See more details below on this page in the section Mechanical angle.

The most commonly-used objectives for (symmetric) diSPIM are 40x water-dipping objectives with a NA of 0.8 (Nikon CFI Apo 40XW NIR). The Olympus 20x/0.5 water objective is another possibility) as is the Nikon 10x/0.3 water. ASI and Special Optics have co-developed two different multi-immersion objectives designed originally for cleared tissue (but useful in any media) that is suitable for the diSPIM geometry. The first with nominal NA 0.4 can image cleared tissue up to 5 mm deep in slab form or within a 12 mm spherical envelope, and the second with nominal NA 0.7 can go 2 mm deep or 10 mm spherical envelope.

Single-sided systems (iSPIM) have much more flexibility because the illumination objective can be a low-NA long-WD objective. A popular pair for high-resolution imaging is the same objective pair as used on the Lattice light sheet, specifically the Nikon 25x/1.1 objective paired with Special Optics 54-10-7 which is 28.6x/0.66.

### Close-up Drawings

### Resolution

Resolution is usually defined as the smallest feature that can be distinguished from a neighboring feature. The diffraction-limited resolution is determined by the objective NA and wavelength; typical equations are 0.61*lambda/NA for lateral resolution and 2*lambda/NA^2 for axial resolution (but there are other expressions depending on the definition chosen). With dual-view systems you can collect datasets from 2 orthogonal directions which can be computationally combined to give “lateral” resolution in 3 axes ^{1)}. Deconvolution can also improve resolution to a certain extent.

Aberrations in the optics or in the sample will degrade the attained resolution. As you image deeper into samples the resolution usually degrades due to scattering, inhomogeneous refractive index within the sample (e.g. cell membrane vs. cytoplasm), and/or mismatch between sample and media refractive index (typically cells are RI ~1.4 vs. media ~1.33).

Undersampling on the camera or in Z step size will decrease attained resolution. The Nyquist criterion applies: the sampling (e.g. pixel size) must be at least half the size of the smallest feature you want to resolve. On the other hand, oversampling in large excess to the Nyquist criterion generates “empty data” where the same amount of information could be contained in a Nyquist-sampled dataset. Thus using improper magnification can degrade resolution. With a 2k x 2k sensor Nyquist tells us that the resolution can be no better than the 0.1% of the field of view.

Resolution does not depend on whether stage scanning or piezo/slice scanning is used as long as the sampling is done correctly. Rather the acquisition method changes the spatial relationship between planes.

### Magnification

Like all infinity microscopes, the magnification is given by the ratio of the effective focal lengths of tube lens and objective. Field of view is just camera sensor size divided by magnification. The sensor size is readily available. The most typical sCMOS cameras have 6.5um square dexels and the sensor comprises an array of 2048×2048 dexels (“dexel” is the more precise term for detection pixel). Other sensor sizes are being used; watch out for 11um square dexels which usually require increasing magnification in order to sample sufficiently for diffraction-limited resolution.

By default ASI uses 200 mm focal length tube lenses (Nikon glass) but a offers a variety of tube lenses so the magnification can easily be chosen otherwise. Typical reasons to adjust the magnification include to adequately sample on the camera (for sensors with larger pixels or using low-mag high-NA objectives) or to increase the field of view by intentionally spatially undersampling ^{2)}.

Note that using Olympus objectives with Nikon tube lens will result in 1.11x increase in magnification. The effective focal length of the cleared tissue objective depends on the media refractive index.

### Mechanical Angle

For traditional SPIM with two orthogonal objectives, the objectives have to be able to co-focus before they mechanically bump ^{3)}. There are details about the tip profiles to consider, but the most important/fundamental factor in whether or not two objectives can be co-focused orthogonally is only indirectly related to the working distance. Rather the condition is simply whether the sum of their mechanical half-angles is less than 90°. For any objective, the mechanical angle must be at least as big as the optical angle, i.e. it must be at least big enough to capture the cone of rays corresponding to its numerical aperture (NA). The mechanical angle is computed as arctan(dia/2/WD) where dia is the diameter of the first surface (assuming the rest of the objective lens fall inside the line from the focal plane to this first surface as is usually the case). The optical (half) angle is computed as arcsin(NA/RI) where RI is the medium refractive index. Some objective lenses have mechanical angles only barely larger than the lower bound optical angle, but others are much less efficient in a mechanical/bulkiness sense.

A detailed overview and helpful table of many objective lenses can be found in Supplementary Note 6 in the Power/Huisken review paper (link to supplemental).

Here are a few objectives that have been used with iSPIM/diSPIM-types systems. Notice that all are used as dipping lenses, even the few that have correction collars.

Objective | Optical angle (NA) | Mechanical angle | Comments |
---|---|---|---|

Nikon 40x/0.8 W | 37° | 42.5° | common high-resolution diSPIM |

Nikon 10x/0.3 W | 13° | 36° | common low-resolution diSPIM |

Olympus 20x/0.5 W | 22° | 45° | fits better than expected (WD is probably a bit more than spec) |

Nikon 25x/1.1 W | 56° | 58° | usual lattice detection |

Olympus 60x/1.1 W | 56° | 57° | usual oSPIM detection, potential lattice detection |

SO 54-10-7 29x/0.66 W | 30° | 30° | usual lattice illumination |

Nikon 20x/1.0 glyc | 43° | 52° | cleared tissue confocal used in light sheet (RI 1.44 - 1.50) |

SO 54-10-12 17x/0.4 MI | 16° | 20° | ASI multi-immersion #1 (RI 1.33 - 1.56, nominal 1.45) |

SO 54-12-8 24x/0.7 MI | 29° | 36° | ASI multi-immersion #2 (RI 1.33 - 1.56, nominal 1.45) |

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