Question

An absorption measurement with a 1 cm path length yields a reading of 0.002 absorbance units with a noise of 0.0005 absorbance units and a mean noise reading of 0 for 5 scans averaged together. Assuming the noise for a single scan does not change if the path length is increased to 5 cm and the number of scans is increase to 65, what is the signal to noise of the new measurement. Remember signal averaging

Answer 1

Assuming the noise remains constant, the total noise for the longer path length, 65 scans should be 0.0005 x 65 = 0.0325 absorbance units. The new reading should be 0.01 absorbance units. The signal to noise ratio (SNR) of the new measurement will be 0.01/0.0325 = 3.08.

Signal averaging decreases the magnitude of the residual noise and increases the SNR. The total noise decreases by the square root of the number of scans, in this case √65 = 8, so for 65 scans, the noise level is 8 times lower than for a single scan.