Light Field Microscopy
Light-field microscope design: lateral sample, resolvable spots per lenslet, matched microlens f-number and the depth of field of refocused slices and single views (Levoy 2006).
Lateral sample on the specimen W/M
7.50 µm
Sparrow limit without lenslets 0.47λ/NA = 1.29 µm
Resolvable spots per lenslet N_u
5.80
diffraction W/R_obj 5.80, pixels W/(2p) 11.54: diffraction limited
Refocused slice depth of field
53.64 µm
(2 + W/R_obj)λn/(2NA²); conventional λn/NA² 13.75 µm
Single-view depth of field
245.2 µm
(2 + N_u²)λn/(2NA²): about N_u non-overlapping refocused slices
Matched microlens f-number
f/50.0
M/(2NA); focal length 7.50 mm for this pitch
Sensor pixels per lenslet
23.1
R_obj = 0.47λM/NA = 25.85 µm in the image
Model
A microlens array sits at the objective's image plane and the sensor one microlens focal length behind it (Levoy et al. 2006). Each lenslet is one spatial sample, W/M on the specimen, and the pixels behind it record the directions. The microlens f-number should equal the objective's image-side f-number M/(2NA), so the micro-images of the objective pupil tile the sensor without overlapping.
Diffraction leaves R_obj = 0.47λM/NA (the Sparrow limit) in the image, so a lenslet of width W holds N_u = W/R_obj resolvable spots: the product of spatial and angular samples is fixed. Resolving them takes about two pixels per spot; Levoy's 15-pixel lenslets resolved about 7 of 11.8 spots, so N_u is capped at W/(2p).
Depth of field is λn/NA² + ne/(M·NA) with e the sample spacing in the image. With e = W, a synthetically refocused slice has (2 + W/R_obj)λn/(2NA²), using the diffraction count even when the pixels limit N_u; a single view, which uses 1/N_u² of the rays, has (2 + N_u²)λn/(2NA²). A focal stack holds about N_u non-overlapping slices.
Spatial–axial trade-off vs microlens pitch
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
Levoy's design equations: Sparrow limit 0.47λM/NA in the image, N_u = W/R_obj (capped at two pixels per spot) and depth of field (2 + W/R_obj)λn/(2NA²) refocused or (2 + N_u²)λn/(2NA²) per view, for N_u ≥ 1. Aberration-free objective; no 3D deconvolution.
- Levoy M., Ng R., Adams A., Footer M., Horowitz M. (2006). Light field microscopy. ACM Trans. Graph. 25(3), 924–934. Eqs. 1–5 and Table 1. doi:10.1145/1141911.1141976
- Ng R., Levoy M., Brédif M., Duval G., Horowitz M., Hanrahan P. (2005). Light field photography with a hand-held plenoptic camera. Stanford Tech. Rep. CTSR 2005-02. Sections 3.1, 3.2 and 4.2. graphics.stanford.edu