Dynamic Range Calculator

Enter the max (non-saturating) signal and the RMS noise floor (often estimated from repeated dark measurements) into the calculator to determine the dynamic range of a spectrometer.

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Dynamic Range Formula

The following formula is used to calculate a dynamic range.

\begin{aligned}
DR &= \frac{MS}{DN}\\
DR_{\text{dB, amp}} &= 20\log_{10}\!\left(\frac{MS}{DN}\right)\\
DR_{\text{dB, power}} &= 10\log_{10}\!\left(\frac{MS}{DN}\right)
\end{aligned}

• Where DR is the dynamic range
• MS is the maximum usable (non-saturating) signal
• DN is the noise floor (commonly the RMS noise / standard deviation of repeated dark measurements; in practice it may include dark noise, read noise, etc.)

To calculate dynamic range as a ratio, divide the max signal by the noise floor. If you need dynamic range in decibels, convert the ratio using 20·log₁₀ for amplitude quantities (e.g., volts, pressure, electron counts) or 10·log₁₀ for power-like quantities (e.g., optical power, luminance).

Dynamic Range Definition

Dynamic range is the ratio between the largest measurable signal (before saturation or clipping) and the smallest signal that can be reliably distinguished from the noise floor. For a spectrometer, this is commonly expressed as the maximum non-saturating signal divided by the RMS noise (often estimated from repeated dark measurements).

Dynamic Range Example

FAQ