Fluorescence Emission Ledger Audit - Biophysical Instrumentation II: From Signals to Genomes Step by Step

A fluorescence readout needs both a per-photon energy gap and a count scaled emitted-energy bundle. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Emission must be lower than excitation in this readout model

The fluorescence helper rejects emitted energy that is not below the excitation energy. The gap is computed before totals are read.

E_{\text{gap}}=E_{\text{excite}}-E_{\text{emit}}

Three excitation-emission pairs close the gap

Each row subtracts emitted energy from excitation energy. The gap column is therefore a checked loss ledger, not a qualitative brightness claim.

\begin{array}{c|c|c}E_{\text{excite}}&E_{\text{emit}}&E_{\text{gap}}\\12\ \text{J}&8\ \text{J}&4\ \text{J}\\15\ \text{J}&5\ \text{J}&10\ \text{J}\\24\ \text{J}&9\ \text{J}&15\ \text{J}\\\end{array}

Photon count scales emitted bundle energy

After the per-photon emitted energy is checked, count scales the total emitted bundle. The count is schematic and integer-only.

\begin{array}{c|c|c}E_{\text{emit}}&N&E_{\text{total}}\\8\ \text{J}&2&16\ \text{J}\\5\ \text{J}&3&15\ \text{J}\\9\ \text{J}&4&36\ \text{J}\\\end{array}

The rendered row closes gap and total

For the rendered row, excitation is 15 J, emission is 5 J, and the count is 3. The gap and total are both computed from those values.

5\ \text{J}+10\ \text{J}=15\ \text{J},\quad 3\cdot5\ \text{J}=15\ \text{J}

Fluorescence closure separates energy gap from brightness

The readout ledger checks energy gap and emitted bundle size. It does not claim detector quantum efficiency, fluorophore chemistry, or real photon joule scales.

E_{\text{emit}}<E_{\text{excite}},\quad E_{\text{total}}=N E_{\text{emit}}