3D Reconstruction Methods

Compare 3D reconstruction approaches: resolution, sampling, voxel budgets, and method tradeoffs.

Number of Z-SlicesZ-Step (µm)XY pixel size at the sample (µm)Numerical ApertureWavelength (nm)Refractive IndexMethodConfocal pinhole (Airy units)Light-sheet NAFOV (µm)

Lateral FWHM

276 nm

pixel ≤ FWHM/2

Axial FWHM

859 nm

z-step > FWHM/2

Total Voxels

100.0M

1000 × 1000 × 100

Volume Size (16-bit)

200.0 MB

Resolution vs NA

Voxel Count vs Z-Step

Method Comparison

Key Formulas

Lateral (widefield, light sheet): FWHM = 0.51 λ/NA

Axial (widefield): FWHM = 0.88 λ/(n − √(n² − NA²))

Confocal: PSF = illumination × (detection ⊗ pinhole); 0.37 λ/NA and 0.64 λ/(n − √(n² − NA²)) as the pinhole → 0

Light sheet: w₀ = λ/(π NA_sheet), FWHM_z = (1/FWHM_sheet² + 1/FWHM_det²)^(−1/2)

Sampling rule of thumb: step ≤ FWHM/2

Volume size: V = N_x × N_y × N_z × 2 bytes

Scalar theory, uniformly filled pupil, no aberrations; the confocal values use equal excitation and emission wavelengths. Deconvolution can sharpen any of these, most of all widefield stacks, which have no optical sectioning.

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

Scalar FWHMs: Airy and sinc² for widefield, the numerical scalar confocal model for 0–5 AU pinholes, and a Gaussian light sheet multiplied with the detection PSF; the light-sheet axial FWHM holds within the sheet's 2z_R, and the sheet thickens beyond it. Sampling uses two samples per FWHM.

Wilson T., Sheppard C. J. R. (1984). Theory and Practice of Scanning Optical Microscopy. Academic Press. Confocal PSF as the product of the illumination PSF and the pinhole-integrated detection PSF.
Wilson T. (2011). Resolution and optical sectioning in the confocal microscope. J. Microsc. 244, 113–121. Lateral, axial and plane responses against pinhole size. doi:10.1111/j.1365-2818.2011.03549.x
Wilhelm R., Gröbler B., Gluch M., Heinz H. (2003). Confocal Laser Scanning Microscopy: Principles. Carl Zeiss. Airy units, the 0.37/0.51 λ/NA and 0.64 limits, and the geometric section formula.
Engelbrecht C. J., Stelzer E. H. K. (2006). Resolution enhancement in a light-sheet-based microscope (SPIM). Opt. Lett. 31, 1477–1479. Axial resolution of sheet × detection PSF. doi:10.1364/OL.31.001477
Born M., Wolf E. (2019). Principles of Optics, 7th ed., §8.5.2 and §8.8. Cambridge University Press. Airy pattern, encircled energy and the defocused PSF. doi:10.1017/9781108769914

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