Stimulated Raman Scattering Microscopy Calculator
Shot-noise-limited SNR, detection limit, Stokes wavelength, resolution and frame time for stimulated Raman scattering microscopy.
Results
ν̃_S = ν̃_p − Ω̃; SRS ∝ Im χ⁽³⁾ · I_p · I_S, with no non-resonant background.
SRG: the Stokes beam gains (pump modulated, Stokes detected). SRL: the pump loses (Stokes modulated, pump detected).
SNR = δ·√N (amplitude ratio; Ozeki et al., Opt. Express 17, 3651, 2009, Eq. 12 quotes its square, the energy ratio δ²N), N = ηPτλ/(hc), shot noise of the detected beam only. Laser excess noise, detector noise and lock-in demodulation losses make real systems worse.
The modulation depth δ depends on the Raman cross-section, the concentration and both intensities: enter a measured or published value, or estimate it from g_R.
Estimate: SRG δ = g_R·F·P̂_p/√2, SRL δ = (λ_S/λ_p)·g_R·F·P̂_S/√2 with F = √2πn/√(λ_p² + λ_S²) for paraxial Gaussian beams of the same far-field angle, a sample thicker than the focus (a liquid) and identical, overlapped Gaussian pulses of peak power P̂. g_R is the plane-wave Stokes gain dI_S/dz = g_R·I_p·I_S (Boyd, Nonlinear Optics, ch. 10); a dilute species scales it by its concentration. Steady-state gain (pulses longer than the Raman dephasing time) and δ ≪ 1.
Focus: Gaussian fit to each beam (Zipfel et al. 2003), signal FWHM of the product I_p·I_S.
Shot-noise SNR vs Pixel Dwell
Detection Limit vs Detected Power
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
SNR = δ√N (amplitude ratio; Ozeki's Eq. 12 is its square, δ²N), shot noise of the detected beam only. δ is an input or a small-signal (δ ≪ 1), steady-state (pulses longer than T₂) estimate from g_R over paraxial Gaussian foci in a thick sample. Excess laser noise and lock-in losses aren't modelled.
- Ozeki Y. et al. (2009). Analysis and experimental assessment of the sensitivity of stimulated Raman scattering microscopy. Opt. Express 17, 3651–3658. Shot-noise-limited SRS sensitivity, Eq. 12. doi:10.1364/OE.17.003651
- Cheng J.-X., Volkmer A., Book L. D., Xie X. S. (2001). An epi-detected coherent anti-Stokes Raman scattering (E-CARS) microscope with high spectral resolution and high sensitivity. J. Phys. Chem. B 105, 1277–1280, p. 1278. A condensed-phase Raman line width is typically ≈ 10 cm⁻¹. doi:10.1021/jp003774a
- Boyd R. W. (2008). Nonlinear Optics, 3rd ed., ch. 10. Academic Press. Stimulated Raman gain dI_S/dz = g_R I_p I_S and the photon-number balance behind SRL.
- Freudiger C. W. et al. (2008). Label-Free Biomedical Imaging with High Sensitivity by Stimulated Raman Scattering Microscopy. Science 322, 1857–1861. SRG and SRL detection with high-frequency modulation. doi:10.1126/science.1165758
- Zipfel W. R., Williams R. M., Webb W. W. (2003). Nonlinear magic: multiphoton microscopy in the biosciences. Nat. Biotechnol. 21, 1369–1377. Gaussian fit to the focus at each wavelength. doi:10.1038/nbt899