Absorbance and transmittance
The instrument compares incident power P0 with transmitted power P. Transmittance is their ratio and decadic absorbance applies a negative logarithm:
T=P0PA=−log10(T)T=10−A A and T are dimensionless. Percent transmittance is %T=100T: for example, T=0.25 corresponds to 25%. The logarithm turns ideal attenuation into a linear relationship with optical path length.
In practice P0 is the blank or reference reading, not the power leaving the source. A slightly negative absorbance is therefore possible: it indicates that the sample transmits somewhat more than the blank, through noise or through its correction.
Beer–Lambert law and units
At a fixed wavelength, absorbance is proportional to concentration and optical path length. Molar and mass concentrations require coefficients with compatible units:
A=ελlcA=aλ∗lρ - ελ: L·mol⁻¹·cm⁻¹, with c in mol/L.
- aλ∗: L·g⁻¹·cm⁻¹, with ρ in g/L.
- With these coefficients, l is expressed in cm. The coefficients depend on the absorbing species and wavelength λ.
For example, ελ=6220Lmol−1cm−1, a 1 cm optical path and c=100μM=10−4mol/L give A=0.622 and approximately 23.88% transmittance.
Assumptions of the ideal model
- Radiation with a sufficiently narrow spectral bandwidth.
- A homogeneous, non-scattering medium and a known optical path.
- A stable absorbing species without interactions that change its coefficient.
- A linear instrument response and appropriately treated blank.
Independent species can contribute additively,Atotal=∑iAi. Distinguishing the components of a mixture requires additional measurements and a suitable model.
Causes of deviation
Stray light compresses high absorbances; broad spectral bandwidth combines different coefficients. Turbidity adds scattering, while chemical equilibria, association, or pH changes may alter the absorbing species. Consequently, no universal absorbance interval guarantees linearity for every instrument and method.
Calibration, interpolation, and dilution
Standards are fitted by ordinary least squares with a free intercept. Standards and sample must share wavelength, optical path length and blank treatment. Concentration is estimated from absorbance and corrected for dilution:
A=mc+bc^=mAs−bc0=c^FD m is the slope, b the intercept and As the sample absorbance. Concentrations use the same unit as the standards; quantification requires m>0.
Comparing this line with A=ελlc identifies the slope: m=ελl, with b=0 in the ideal case. The common optical path of the standards therefore yields ελ from the slope, and a non-zero intercept points to a contribution other than the analyte.
The dilution factor FD is the ratio of final volume to aliquot volume in a simple dilution. Bringing 1 mL of sample to a final volume of 10 mL gives FD=10. c^ refers to the measured aliquot and c0 to the original sample.
Interpolation occurs only when c^ lies between the minimum and maximum standards. Outside that domain, extrapolation extends the line mathematically but adds uncharacterized uncertainty. If As falls below b, the inversion returns a negative value, which does not represent a concentration: it points to a sample below the calibrated range, or to a blank or baseline problem.
Residuals, R², and intercept
Residuals ei=Ai−A^i are differences between measured and predicted absorbances. They help examine curvature, changes in scatter and points away from the general pattern. A high R² does not by itself validate linearity, matrix effects, blank treatment or precision.
If the 95% confidence interval for the intercept excludes zero, the blank or matrix may contribute. The fit alone does not identify the cause.
Detection and quantification limits
The limit of detection (LOD) refers to the lowest detectable concentration; the limit of quantification (LOQ), to the lowest quantifiable concentration with suitable precision and accuracy. With residual standard deviation sy/x and slope m>0:
LODest=3.3msy/xLOQest=10msy/x These estimates depend on the calibration range and experimental design. Confirmation requires samples of known concentration near the limits and evidence of suitable precision and accuracy; fitting a line alone does not demonstrate that performance.
Scope and references
OD600 primarily depends on scattering. For nucleic acids, A260 can estimate concentration with appropriate factors and corrections; A260/A280 is an indicator of purity. That ratio alone does not determine concentration.