Cleared Tissue Imaging Calculator

Cleared tissue imaging: ballistic light fraction with depth, resolution, and the focal shift from an index mismatch.

Objective NAWavelength (nm)Sample (clearing medium) index n_sObjective immersion index n_immDepth in the tissue (µm)Absorption µ_a (mm⁻¹)Scattering µ_s (mm⁻¹)

Results

Lateral resolution λ/(2NA)283 nm

Axial FWHM, widefield PSF (index-matched)1.019 µm

Ballistic fraction at depth60.0 %

Ballistic loss2.2 dB

Scattering length 1/µ_s2.00 mm

Depth to 1/e (1/µ_t)1.96 mm

Depth to 1 %9.03 mm

Focal shift factor, paraxial n_s/n_imm1.000×

Focal shift factor, marginal ray1.000×

Ballistic fraction vs depth

Model

Ballistic fraction = exp(−(µ_a + µ_s) z)

Axial FWHM = 0.88 λ/(n_s − √(n_s² − NA²)); lateral = λ/(2NA)

Focal shift: n_s/n_imm (paraxial) to tan α_imm/tan α_s (marginal ray), sin α = NA/n

Clearing lowers µ_s by matching the refractive indices inside the tissue; the default µ_a and µ_s are example values for a well-cleared sample, not measured data. The ballistic fraction is the unscattered light that still forms a sharp focus, one way at this wavelength; scattered light adds a diffuse background and is not counted. The resolution figures hold for an objective matched to the sample. When n_imm ≠ n_s, the focus moves by a factor between the two shift factors per unit of stage travel (scale z-stacks by it), and spherical aberration broadens the PSF with depth, which this page does not model.

Model and references

Textbook approximation. A standard approximation from the literature (for example paraxial, plane-wave or Gaussian-beam), valid within the range the page states. About the tiers

Beer–Lambert attenuation of ballistic light only (scattered light is not counted). Resolution assumes an index-matched objective; the mismatch focal shift is bounded by the paraxial and marginal-ray factors, and spherical aberration is not modelled. Default µa and µs are examples.

Jacques S. L. (2013). Optical properties of biological tissues: a review. Phys. Med. Biol. 58, R37–R61. Absorption and scattering coefficients. doi:10.1088/0031-9155/58/11/R37
Richardson D. S., Lichtman J. W. (2015). Clarifying tissue clearing. Cell 162, 246–257. Refractive-index matching and scattering in cleared tissue. doi:10.1016/j.cell.2015.06.067
Hell S., Reiner G., Cremer C., Stelzer E. H. K. (1993). Aberrations in confocal fluorescence microscopy induced by mismatches in refractive index. J. Microsc. 169, 391–405. Focal shift. doi:10.1111/j.1365-2818.1993.tb03315.x
Diel E. E., Lichtman J. W., Richardson D. S. (2020). Tutorial: avoiding and correcting sample-induced spherical aberration artifacts in 3D fluorescence microscopy. Nat. Protoc. 15, 2773–2784. Paraxial and marginal-ray focal-shift factors. doi:10.1038/s41596-020-0360-2
Born M., Wolf E. (2019). Principles of Optics, 7th ed., §8.8. Cambridge University Press. Axial PSF of a uniformly filled pupil. doi:10.1017/9781108769914

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