The capstone of the spectrophotometry set. Instead of computing absorbance the textbook way — A = log₁₀(I₀/I), which bends away from linearity above A ≈ 1–2 — the TFit method fits a model of the instrument-broadened transmission spectrum to the raw measurement, recovering the true absorbance free of stray-light and polychromatic error. The payoff is hyperlinear calibration: a straight line over a 10,000× range. Set the peak and slit widths, add stray light and noise, and watch TFit hold the line while the classic methods roll off.
Drag across the plot to move the true-absorbance marker. Dashed diagonal = ideal (measured = true).
True A—
Single-λ log A—
CLS—
TFit—
Same law, computed better — a straight line across 10,000×. TFit doesn't reject Beer's law; it's built on it. The old log₁₀(I₀/I) definition was a 1729 convenience chosen because a logarithm was easy to compute by hand — but it silently assumes the light is perfectly monochromatic and there's no stray light. TFit drops those assumptions by fitting the actual transmission the instrument records, so the calibration stays linear far past where log-absorbance bends over. Wider linear range means fewer standards, less dilution, and freedom to open the slit for a better signal-to-noise ratio.
How It Works
Model the transmission the instrument really records, then fit it.
1
Why log(I₀/I) bends
A real spectrometer passes a band of wavelengths and the detector averages transmittance, not absorbance. When the peak is strongly absorbed, its wings still leak light through the slit, so the measured transmission reads too high and the absorbance too low. Stray light adds a floor. Both pull the single-wavelength log curve (red) below the true value at high absorbance.
2
Fit, don't log
TFit takes the analyte's reference shape, scales it by a trial coefficient, converts to transmission, convolves it with the measured slit function and adds the stray light — reproducing exactly what the instrument would record — then adjusts the coefficient by least squares until the model matches the data. The best-fit coefficient (green) is the true absorbance, and it tracks the ideal diagonal.
3
Push it to the limits
Widen the slit relative to the peak, or add stray light, and the red and cyan curves roll off sooner — while TFit holds. Add noise and TFit eventually breaks too, at the far extreme where the transmission barely changes with concentration. Nothing is infinite, but TFit buys roughly two extra decades of usable, linear range.
What is the transmission-fitting (TFit) method?
A way to do quantitative absorption spectrophotometry that computes absorbance by fitting a model of the instrument-broadened transmission spectrum to the measured transmission, instead of the textbook A = log₁₀(I₀/I). It scales the analyte reference by a coefficient, converts to transmission, convolves with the slit function, adds stray light, and least-squares fits the coefficient — which then equals the true absorbance free of polychromatic and stray-light error. Developed by Tom O'Haver.
Why does log(I₀/I) absorbance go non-linear at high values?
Because the instrument passes a band of wavelengths and the detector averages transmittance, not absorbance. At high absorbance the peak transmits almost nothing but the band's wings still leak light, so measured transmission is too high and absorbance too low; stray light adds a fixed floor. Together they bend log(I₀/I) below the true value, usually from around A = 1–2.
What does hyperlinear calibration mean?
Linear over a far wider range than usual — with TFit, up to roughly 10,000× in absorbance, versus the ~100× useful range of conventional absorbance. That means fewer standards, less dilution, and the freedom to widen the slit for a better signal-to-noise ratio.
Does TFit replace the Beer–Lambert law?
No — it's based on Beer's law. TFit just calculates the absorbance a different way, one that doesn't assume stray light and polychromatic radiation are zero. The log(I₀/I) definition was a 1729 convenience chosen for easy hand computation; TFit uses modern computation to model the measurement fully and recover the absorbance Beer's law predicts under ideal conditions.
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