Stray Light & Order Overlap Calculator
Absorbance error and highest readable absorbance from a spectrophotometer's stray light ratio, and the grating orders that overlap a set wavelength.
Photometric Error
Measured Transmittance
0.001999
true 0.001000; (1 − s)T + s·T_s
Measured Absorbance
2.699 AU
−log₁₀ T_m
Absorbance Error ΔA
-0.301 AU
-10.0 % of A, read as concentration
Highest Readable Absorbance
3.000 AU
A_max = −log₁₀(s·T_s), as A → ∞
Largest s for |ΔA| ≤ 0.01 AU at A = 3
0.0000233 (0.00233 %)
T(10^δ − 1)/(T_s − T)
Stray Light Level (optical density)
OD 3.00
−log₁₀ s, the rejection quoted for monochromators
Measured vs True Absorbance
Absorbance Error ΔA = A_m − A
Order Overlap
Order-Sorting Filter Pass Band
300.0 – ∞ (long-pass)
a long-pass above mλ/(m + 1) is enough in first order
Overlap-Free Band in 200–1100 nm (order 1)
200.0 – 400.0 nm
from max(λ_min, λ_max(m − 1)/m) to λ_min(m + 1)/m or λ_max
Wavelengths Arriving with 600 nm (order 1)
- Order 2: 300.0 nm
- Order 3: 200.0 nm
Model
T_m = (1 − s)·T + s·T_s, A_m = −log₁₀ T_m, ΔA = −log₁₀(1 − s + s·T_s·10^A), A_max = −log₁₀(s·T_s)
n·λ′ = m·λ (same diffraction angle at a fixed grating setting)
s is the stray radiant power ratio: stray power divided by the total power detected in the reference (blank) measurement. The opaque-filter method of ASTM E387 measures it as the reading through a cut-off filter that blocks the set wavelength but passes the stray light, divided by the blank reading. The sample attenuates the in-band light by T = 10^−A and the stray light by T_s; T_s = 1 (sample transparent where the stray light lies) is the usual worst case. Some texts give the stray power relative to the in-band power, S = P_s/P₀, and write T_m = (T + S·T_s)/(1 + S); that is the same model with s = S/(1 + S). With T_s > T, stray light makes high absorbances read low, which bends a Beer–Lambert calibration line towards A_max.
At a fixed grating angle, order n of λ′ = mλ/n leaves along the same direction as order m of λ, whatever the groove density. These overlapping orders are not grating ghosts: ghosts (Rowland, Lyman) come from periodic ruling errors and are not modelled here, nor is the spectrum of the scattered light.
References: ASTM E387, Standard Test Method for Estimating Stray Radiant Power Ratio of Dispersive Spectrophotometers by the Opaque Filter Method; D. A. Skoog, F. J. Holler, S. R. Crouch, Principles of Instrumental Analysis, ch. 13; C. Palmer, E. Loewen, Diffraction Grating Handbook, 6th ed. (Newport, 2005), ch. 2.
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
Stray light is a fixed fraction s of the detected reference power, attenuated by one effective sample transmittance; its spectrum, the slit function and true ruling-error ghosts are not modelled. Order overlap is exact for a fixed grating angle.
- ASTM E387-04 (reapproved 2022). Standard Test Method for Estimating Stray Radiant Power Ratio of Dispersive Spectrophotometers by the Opaque Filter Method. ASTM International. doi:10.1520/E0387-04R22
- Skoog D. A., Holler F. J., Crouch S. R. Principles of Instrumental Analysis, ch. 13 (stray radiation). Cengage.
- Palmer C., Loewen E. (2005). Diffraction Grating Handbook, 6th ed., ch. 2. Newport.