Fig 1.
Five different illumination geometries common for light microscopy.
Fig 2.
Generalised optical microscope.
Illumination and detection optics can be at a relative angle. Without loss of generality, the magnification is assumed to be equal to one.
Fig 3.
Boundary and source of the heat equation for line-confocal illumination.
Left: cuboid sample (∞ × 2l × 2l) surrounded by a thermal reservoir of temperature u0 and typical illumination shape IP(r,t) of a line-confocal microscope. Right: evolution of irradiance with illumination period T.
Table 1.
Strategies to solve the heat equation for a wide range of illumination periods T and different illumination geometries.
Table 2.
Waist diameter of the elliptic Gaussian beam defining the illumination geometry IP(r).
Fig 4.
Maximal permissible peak irradiance IP0(T) for five different illumination geometries depending parametrically on the illumination period T using a 0.8 NA lens.
The sample is assumed to consist mainly of water. The vacuum illumination wavelength is chosen to be λ = 550 nm. The maximal permissible temperature rise is arbitrarily set to ucrit - u0 = 10 K and the absorption coefficient is set to μa = 1 mm-1. Solid lines describe infinitely extended samples (heat never reaches the thermal reservoir) and dashed lines describe samples of a finite size with a cuboid shape: 2l × 2l × ∞ for line-confocal and line illumination and 2l × ∞ × ∞ for light sheet illumination. Results of the thermally stationary state are calculated with FEM and match the analytical solution.
Fig 5.
Temperature factor uf(T) for five different illumination geometries depending parametrically on the illumination period T using a 0.8 NA lens.
Like Fig 4 but normalised against the absorption coefficient μa and the maximal permissible temperature rise (ucrit - u0).
Table 3.
The illumination period T is given by the total 2D image acquisition time T0.
Fig 6.
Theoretical SNRN comparison of aqueous sample images consisting of 1000 × 1000 spectra, using a 0.8 NA objective lens.
We assume an illumination wavelength of λ = 550 nm, temperature limited irradiance, ideal hyperspectral sensors (except grey line): efficiency η = 1 and a noise condition parameter qs = 0. Solid lines describe infinitely extended samples (heat never reaches the thermal reservoir) and dashed lines describe samples of a finite size with cuboid shape: 2l × 2l × ∞ for line-confocal and line illumination and 2l × ∞ × ∞ for light sheet illumination. The grey curve represents a light sheet system equipped with a 1000 channel filter based hyperspectral detector. Assuming a constant spectral light distribution and shot noise only the SNR drops by a factor of square root of 1000 compared to the ideal hyperspectral detector (red curve). Notice: the irradiance is adjusted parametrically with acquisition time T0 according to Fig 5, to always meet the permissible temperature rise in the sample.
Fig 7.
Like Fig 6 but for 50 × 50 spectra.
Notice, that for a shrinking number of pixels (accompanied by a shrinking field of view), all methods (apart from grey) exhibit similar performance (graphs shift along T0) because they become essentially more and more scanning approaches.