Calculators for spectrometer design, spectroscopy fundamentals, and signal analysis.
41 calculators
Planck's law spectral radiance, Wien peak wavelength, Stefan-Boltzmann radiant exitance and radiance, and the fraction of power in any wavelength band.
FTIR spectral resolution from maximum OPD, apodization (Norton–Beer, Happ–Genzel, Blackman–Harris) and scan parameters, with computed instrument line shapes.
Beer-Lambert law A = ε·c·l: solve for absorbance, concentration or the molar absorption (extinction) coefficient, with transmittance, mass concentration and mass absorption coefficient; and the transmittance of a bulk sample from its absorption coefficient α and thickness.
σ = ε · 1000 · ln(10) / N_A — convert the molar absorption (extinction) coefficient to the cross-section per molecule and back, with number density and Napierian absorption coefficient.
Absorption depth δ = 1/α, the depth for 90 % absorption and the fraction absorbed in a layer, from measured α(λ) of silicon (Green 2008) and water (Pope & Fry, Segelstein) or your own α.
Compare 9 window functions and their instrument line shapes (ILS). Select windows to overlay.
Model CRDS ring-down time, sensitivity, and finesse. Visualize exponential decay with and without sample absorption.
Solid angle, f-number and slit étendue of a spherical-mirror spectrometer, with its slit-limited resolving power and the Jacquinot advantage of an FTIR of the same aperture.
Diffraction grating parameters: grating equation, angular/linear dispersion, blaze profile.
Model dual-comb spectroscopy parameters: resolution, bandwidth, update rate, and multi-heterodyne RF spectrum.
XPS and UPS photoelectrons: kinetic energy E_k = hν − E_B − φ_sp, inelastic mean free path from the TPP-2M equation, sampling depth 3λ cos θ and the kinetic energies from common X-ray and UV sources.
Fabry-Pérot etalon: FSR = λ²/(2nd cos θ). Transmission follows the Airy function.
Model single and bi-exponential fluorescence decay curves. Calculate intensity-weighted average lifetimes.
Relative fluorescence quantum yield against a reference standard: Φ = Φ_ref (F_s/F_ref)(f_ref/f_s)(n_s/n_ref)² with absorbed fractions f = 1 − 10^−A, compared with the absorbance-ratio approximation.
Sample two sinusoids plus white noise and read their amplitudes from a windowed FFT: bin spacing, Nyquist aliasing, scalloping and the noise floor.
Scalar blaze efficiency of a ruled grating in Littrow versus wavelength, with the order cutoff and Rayleigh anomalies.
Vibration–rotation band of HCl or CO: anharmonic band origin, P and R branch lines, Boltzmann intensities at the instrument resolution, force constant and the isotope shift of H³⁷Cl or ¹³CO.
Maximum solid angle of an FTIR interferometer, Ω = 2π/(ν̃·L) with L the maximum OPD, which sets its throughput advantage over a grating spectrometer.
Laser-Induced Breakdown Spectroscopy: Stark width from electron density or electron density from a measured Stark width, Doppler and instrument widths, the Saha ionisation ratio and the McWhirter LTE check.
Interferogram of Gaussian spectral lines and the spectrum recovered by cosine transform: resolution 1/L, resolving power, Nyquist aliasing and fringe visibility. Two-beam fringes of a Michelson or Mach-Zehnder interferometer with their visibility.
Pure rotational spectrum of a diatomic molecule: B from the masses and bond length, B_v with α_e, line frequencies 2B(J+1) − 4D(J+1)³, Boltzmann populations and absolute line intensities S in HITRAN units, with CO and HCl presets.
NIR spectroscopy: measured water absorption bands and transmittance from 780 to 2500 nm, Morse overtone positions, and haemoglobin changes from the two-wavelength modified Beer–Lambert law with an age-dependent DPF.
Convert optical density, transmission, attenuation in dB and filter factor (photographic stops) with presets.
Optical path length nL through a slab crossed N times at any incidence angle, with the phase delay OPL/c, the group delay n_g L/c and the extra delay against vacuum; n and n_g from Sellmeier data for common glasses.
Optical penetration depth from the complex index n + ik at any angle of incidence: d_p = λ₀/(4π Im √(N² − n₀² sin²θ)), covering absorbing media, metals (skin depth) and total internal reflection.
Mertz and Forman phase correction run on a simulated single-sided FTIR interferogram with ZPD offset, phase offset, dispersion and noise, compared with the magnitude spectrum.
Pump-probe and transient absorption with sequential A → B → ground-state kinetics: ΔA kinetic traces and spectra in mOD from the pump fluence and ε, with bleach, stimulated emission and excited-state absorption bands and the pump-probe cross-correlation.
Convert between Raman shift (cm⁻¹) and Stokes or anti-Stokes wavelength for any laser, with the vibrational energy and the anti-Stokes/Stokes ratio.
Wavelength calibration of a Czerny–Turner spectrograph from mercury lines: linear, quadratic and cubic fits against the grating-equation pixel map.
Overlapping Gaussian, Lorentzian or pseudo-Voigt bands: areas, band width and centroid, whether neighbours resolve, and least-squares heights with standard errors from a simulated noisy spectrum; or a vibronic (Huang–Rhys) absorption and emission band with its Stokes shift.
Doppler, pressure and natural line widths and the exact Voigt profile, with the Olivero and pseudo-Voigt (TCH) approximations; or combine any Gaussian and Lorentzian widths.
Spectral coverage, resolution, and dispersion for a grating-based spectrometer.
Compare spectral resolution across grating, prism, and Fabry-Pérot spectrometers.
Δν̃ = ν̃_abs − ν̃_em — energy difference between absorption and emission maxima.
Absorbance error and highest readable absorbance from a spectrophotometer's stray light ratio, and the grating orders that overlap a set wavelength.
SFG vibrational spectrum of an interface: the SFG wavelength and |χ⁽²⁾|² of Lorentzian CH or OH resonances interfering with a non-resonant background of chosen amplitude and phase.
Electromagnetic SERS enhancement factor of a silver nanosphere: local field, maximum and surface-averaged |E|⁴ enhancement, resonance and distance decay.
THz time-domain transmission of a slab: n and α of liquid water (double Debye), a phonon mode (Lorentz) or a constant medium, Fresnel losses, time delay, the extraction n = 1 + cφ/(ωd) and the dynamic-range limit on α.
Time-correlated single photon counting: one- or two-exponential decays convolved with a Gaussian IRF in closed form, the decay left over from earlier pulses at the repetition rate, the centroid shift and the laser's transform-limited bandwidth.
Absorptive 2D electronic spectrum of a coupled dimer: exciton splitting √(Δ² + 4J²), bleach, stimulated-emission and excited-state-absorption peaks, energy transfer during the waiting time and homogeneous vs inhomogeneous lineshapes.
Convert wavelength, wavenumber, frequency, and energy with sliders, presets, and range sweeps.